%!PS-Adobe /wpdict 120 dict def wpdict begin /bdef {bind def} bind def /bflg false def /Bfont 0 def /bon false def /psz 0 def /_S /show load def /_t {0 rmoveto} bdef /_pixelsnap {transform .25 sub round .25 add exch .25 sub round .25 add exch itransform } bdef /_pixeldsnap { dtransform round exch round exch idtransform } bdef /_lt {_pixelsnap lineto} bdef /_rlt {_pixeldsnap rlineto} bdef /_mt {_pixelsnap moveto} bdef /_rmt {_pixeldsnap rmoveto} bdef /bshow {gsave psz 30 div 0 _rmt dup show grestore show} bdef /DUx 0 def /DUy 0 def /hscl 0 def /M {_mt 2 mul -2 2 { -2 roll 0 _rmt _S } for } bdef /makeoutl { dup /OutlineFlag known not { dup dup length 2 add dict begin {1 index /FID ne { def }{ pop pop } ifelse } forall /UniqueID known {/UniqueID UniqueID 10000 add def} if /PaintType PaintType 0 eq { 2 }{ PaintType } ifelse def /StrokeWidth 15 def /OutlineFlag true def /OutlineFont currentdict end definefont } if } bdef /nbuff 50 string def /orntsv 0 def /plen 0 def /pwid 0 def /picstr 1 string def /WPencoding StandardEncoding 256 array copy def 0 [ 127/Aacute/Acircumflex/Adieresis/Agrave/Aring/Atilde/Ccedilla /Delta/Eacute/Ecircumflex/Edieresis/Egrave/Eth/Gamma/Iacute /Icircumflex/Idieresis/Igrave/Lambda/Ntilde/Oacute /Ocircumflex/Odieresis/Ograve/Omega/Otilde/Phi/Pi/Psi /Scaron/Sigma/TeXtext32/Theta/Thorn 209/Uacute/Ucircumflex/Udieresis/Ugrave/Upsilon/Xi/Yacute /Ydieresis/Zcaron/aacute/acircumflex/adieresis/agrave /aring/atilde/brokenbar 228/ccedilla/copyright/degree/divide 236/dotlessj/eacute/ecircumflex/edieresis/egrave 242/eth/ff/ffi 246/ffl/iacute 252/icircumflex/idieresis/igrave/logicalnot 1/minus/mu/multiply/ntilde/oacute/ocircumflex/odieresis /ograve/onehalf/onequarter/onesuperior/otilde/plusminus /registered/scaron/thorn/threequarters/threesuperior /trademark/twosuperior/uacute/ucircumflex/udieresis /ugrave/yacute/ydieresis/zcaron ] { dup type /nametype eq { WPencoding 2 index 2 index put pop 1 add } { exch pop } ifelse } forall pop /reencode { dup FontDirectory exch known { findfont } { dup nbuff cvs dup length 1 sub get 82 eq {dup nbuff cvs dup length 1 sub 0 exch getinterval findfont begin currentdict dup length dict begin { 1 index /FID ne {def} {pop pop} ifelse } forall /FontName exch def /Encoding WPencoding def currentdict dup end end /FontName get exch definefont } { findfont } ifelse } ifelse } bdef /WPDLencoding StandardEncoding 256 array copy def 0 [ 127 /SA420000/SD630000/SF010000/SF020000/SF030000 /SF040000/SF050000/SF060000/SF070000/SF080000/SF090000 /SF100000/SF110000/SF140000/SF150000/SF160000/SF190000 /SF200000/SF210000/SF220000/SF230000/SF240000/SF250000/SF260000 /SF270000/SF280000/SF360000/SF370000/SF380000/SF390000/SF400000 /SF410000/SF420000/SF430000 209 /SF440000/SF450000/SF460000/SF470000/SF480000 /SF490000/SF500000/SF510000/SF520000/SF530000/SF540000 /SF570000/SF580000/SF590000/SF600000/SF610000 228 /SM570001/SM590000/SM600000/SM630000 236 /SM680000/SM690000/SM700000/SM750000/SM750002 242 /SM770000/SM790000/SP320000 246 /SS000000/SS010000 252 /SS260000/SS270000/SV040000/apostrophereverse 1/arrowboth/arrowdown/arrowleft/arrowright/arrowup/club /deutschmark/diamond/diamondopen/exclamdbl/female /fiveeighths/franc/heart/male/musicalnote/musicalnotedbl /napostrophe/nsuperior/oneeighths/seveneighths/spade /threeeights/underscoredbl/SM760000 ] { dup type /nametype eq { WPDLencoding 2 index 2 index put pop 1 add } { exch pop } ifelse } forall pop /reencodeL { dup FontDirectory exch known { findfont } { dup nbuff cvs dup length 1 sub get 76 eq { dup nbuff cvs dup length 1 sub 0 exch getinterval findfont begin currentdict dup length dict begin { 1 index /FID ne {def} {pop pop} ifelse } forall /FontName exch def /Encoding WPDLencoding def currentdict dup end end /FontName get exch definefont } { findfont } ifelse } ifelse } bdef /ron false def /sflg false def /slan 0 def /sp 32 def /sshow { save exch gsave psz 20 div dup neg _rmt dup show grestore dup save exch Bfont setfont 1 setgray show restore currentfont makeoutl setfont show currentpoint 3 -1 roll restore _mt } bdef /Sx 0 def /Sy 0 def /Ux 0 def /Uy 0 def /W /widthshow load def /_B {/bflg true def sflg not {/_S /bshow load def /bon true def} if } bdef /_b {/bflg false def bon {/_S /show load def /bon false def} if } bdef /_bd {save} bdef /_bp {save 2 setmiterlimit .06 .06 scale 0 0 _mt} bdef /_ccprocs {/proc2 exch cvlit def /proc1 exch cvlit def /newproc proc1 length proc2 length add array def newproc 0 proc1 putinterval newproc proc1 length proc2 putinterval newproc cvx } def /_clr {3 {255 div 3 1 roll} repeat ron {6 3 roll pop pop pop} {setrgbcolor} ifelse } bdef /_cp /closepath load def /_cw {stroke initclip _mt 0 2 index _rlt 0 _rlt 0 exch neg _rlt clip newpath } bdef /_d /setdash load def /_DU {currentpoint /DUy exch def /DUx exch def} bdef /_du {gsave save 8 setlinewidth currentpoint -30 add _mt DUx DUy -30 add _lt stroke restore 8 setlinewidth currentpoint -50 add _mt DUx DUy -50 add _lt stroke grestore } bdef /_ed {restore} bdef /_ep {restore showpage 0 0 _mt} bdef /_f /eofill load def /_ff { exch reencode exch 3 div dup /psz exch def scalefont dup /Bfont exch def setfont } bdef /_ffs { /slan exch 10 div def /hscl exch 1000 div def /psz exch 3 div def [ psz hscl mul 0 slan dup sin exch cos div psz mul psz 0 0 ] exch reencode exch makefont dup /Bfont exch def setfont } bdef /_g /setgray load def /_gs {neg 100 add 100 div setgray} bdef /_i {gsave dup /picstr exch 7 add 8 idiv string def 3 1 roll translate dup 1 scale dup 1 1 [5 -1 roll 0 0 1 0 0] {currentfile picstr readhexstring pop} image grestore } bdef /_is {save 4 1 roll dup /picstr exch 7 add 8 idiv string def 3 1 roll translate dup 1 scale dup 1 1 [5 -1 roll 0 0 1 0 0] {currentfile picstr readhexstring pop} image restore } bdef /_ie {1 eq { {1 exch sub} currenttransfer _ccprocs settransfer} if /_isx exch def /_isy exch def _isx mul exch _isy mul translate add 2 div /_txc exch def add 2 div /_tyc exch def _txc _isx mul _tyc _isy mul translate 360 exch sub rotate 1 eq { _isx neg _isy scale } { _isx _isy scale } ifelse _txc neg _tyc neg translate } bdef /_irms {save 12 1 roll 1 eq {{1 exch sub} currenttransfer _ccprocs settransfer} if /picstr exch string def translate 2 index 6 index sub 2 div 2 index 6 index sub 2 div neg translate 5 index 5 index 2 div neg exch 2 div exch 2 copy neg exch neg exch 5 2 roll translate 360 exch sub rotate 3 index 3 index 7 index div exch 8 index div exch scale translate pop pop 2 index 2 index scale 3 index 0 eq { [ 3 index 0 0 5 index neg 0 0 ] } { 3 index 1 eq { [ 3 index 0 0 5 index 0 7 index ] } { 3 index 128 eq { [ 3 index neg 0 0 5 index neg 7 index 0 ] } { [ 3 index neg 0 0 5 index 7 index 7 index ] } ifelse } ifelse } ifelse {currentfile picstr readhexstring pop} image pop restore } bdef /_l {_lt} bdef /_lr {_rlt} bdef /_m {_mt} bdef /_O {currentfont makeoutl setfont} bdef /_o {Bfont setfont} bdef /_ornt {/pwid exch def /plen exch def orntsv 1 eq {0 pwid translate -90 rotate} if orntsv 2 eq {pwid plen translate 180 rotate} if orntsv 3 eq {plen 0 translate 90 rotate} if dup 1 eq {pwid 0 translate 90 rotate} if dup 2 eq {pwid plen translate 180 rotate} if dup 3 eq {0 plen translate -90 rotate} if /orntsv exch def } bdef /_lod1 {currentpoint orntsv plen pwid 6 -1 roll restore save} bdef /_lod2 {_bp 7 2 roll _ornt _mt} bdef /_unlod {currentpoint orntsv plen pwid 7 -2 roll restore restore _bp 6 1 roll _ornt _mt } bdef /_p {2 copy _mt 1 0 _rlt _mt} bdef /_pl {{_lt} repeat} bdef /_R { /ron true def /_S /_rshow load def /_t /_red load def} bdef /_rshow { save exch currentpoint /RSy exch def /RSx exch def ron { sflg { currentpoint /Ry exch def /Rx exch def dup stringwidth pop Rx Ry psz 4 div add _mt Rx psz 15 add setlinewidth .95 setgray 0 setlinecap add Ry psz 4 div add _lt stroke Rx Ry _mt 0 0 0 setrgbcolor dup show Rx Ry _mt sshow } { _redshow }ifelse } { sflg {sshow} if }ifelse currentpoint 3 -1 roll restore _mt } bdef /_red { gsave dup currentpoint /Ry exch def /Rx exch def Rx Ry psz 4 div add _mt Rx psz 15 add setlinewidth .95 setgray 0 setlinecap add Ry psz 4 div add _lt stroke Rx Ry _mt grestore 0 rmoveto }bdef /_redshow {currentpoint /Ry exch def /Rx exch def dup stringwidth pop Rx Ry psz 4 div add _mt Rx psz 15 add setlinewidth .95 setgray 0 setlinecap add Ry psz 4 div add _lt stroke Rx Ry _mt 0 0 0 setrgbcolor show currentpoint _mt }bdef /_rmxy {_rmt} bdef /_s /stroke load def /_SH bon {/bon false def} if {/sflg true def /_S /_rshow load def } bdef /_sh { ron {/sflg false def bflg {_B} if} {/_S /show load def /sflg false def bflg {_B} if}ifelse }bdef /_sp { gsave stroke grestore } bdef /_ST {currentpoint /Sy exch def /Sx exch def} bdef /_st {gsave currentpoint pop Sx dup Sy _mt sub (\320) stringwidth pop div dup floor cvi dup dup 0 gt {{(\320) show} repeat}{pop} ifelse sub dup 0 gt {1 scale (\320) show}{pop} ifelse grestore } bdef /_U {currentpoint /Uy exch def /Ux exch def} bdef /_u {gsave currentpoint -30 add _mt Ux Uy -30 add _lt 12 setlinewidth stroke grestore } bdef /_w /setlinewidth load def end /#copies 1 def wpdict begin _bd /_ieq {gsave dup /picstr exch 7 add 8 idiv string def 3 1 roll translate dup 1 scale dup 1 false [5 -1 roll 0 0 1 0 0] {currentfile picstr readhexstring pop} imagemask grestore} bdef letter _bp 0 13200 10200 _ornt /Times-RomanR 550 _ff 0 13200 10200 _ornt /_r { sflg {/_t {0 rmoveto}bdef /ron false def} { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse }bdef 3534 11865 _m /Times-BoldR 825 _ff (NNES)_S 92 _t (USER'S)_S 92 _t (MANUAL)_S /Times-RomanR 550 _ff 3485 11505 _m (Copyright)_S 61 _t (\345)_S 61 _t (March)_S 61 _t (31,)_S 61 _t (1993)_S 61 _t (by)_S 61 _t (R.S.)_S 61 _t (Bain)_S 1200 11145 _m /Times-BoldR 550 _ff (Table)_S 61 _t (of)_S 61 _t (Contents)_S /Times-RomanR 550 _ff 1800 10785 _m (Introduction)_S 61 _t 8400 10785 _m 61 _t (1)_S 1200 10425 _m (1)_S 1800 10425 _m (Using)_S 61 _t (NNES)_S 61 _t (with)_S 61 _t (Default)_S 61 _t (Settings)_S 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801 _cw _s grestore 3359 2850 _m (Figure)_S 61 _t (1)_S 122 _t (Step)_S 61 _t (for)_S 61 _t (Absolute)_S 61 _t (Newton's)_S 61 _t (Method)_S 1800 2450 _m (The)_S 54 _t (lower)_S 55 _t (bound)_S 55 _t (for)_S 54 _t (X1)_S 55 _t (has)_S 55 _t (been)_S 54 _t (violated)_S 55 _t (by)_S 55 _t (amount)_S 54 _t /HelveticaR 600 _ff (a)_S /Times-RomanR 550 _ff 55 _t (and)_S 54 _t (the)_S 55 _t (upper)_S 55 _t (bound)_S 54 _t (for)_S 55 _t (X2)_S 55 _t (has)_S 1800 2250 _m (been)_S 90 _t (violated)_S 90 _t (by)_S 90 _t (amount)_S 90 _t /HelveticaR 600 _ff (b)_S /Times-RomanR 550 _ff 90 _t (by)_S 90 _t (the)_S 90 _t (proposed)_S 91 _t (full)_S 90 _t (Newton)_S 90 _t (step.)_S 180 _t (The)_S 90 _t (amount)_S 90 _t (of)_S 90 _t (the)_S 1800 2050 _m (violation)_S 45 _t (for)_S 44 _t (each)_S 44 _t (component)_S 45 _t (is)_S 44 _t (reflected)_S 44 _t (in)_S 45 _t (the)_S 44 _t (respective)_S 45 _t (bound)_S 44 _t (to)_S 45 _t (obtain)_S 44 _t (the)_S 45 _t (shorter)_S 44 _t (step)_S 1800 1850 _m (of)_S 61 _t (the)_S 61 _t (Absolute)_S 61 _t (Newton's)_S 61 _t (method.)_S 4932 1250 _m (-)_S 61 _t (3)_S 61 _t (-)_S _ep _bp /Times-RomanR 550 _ff 0 13200 10200 _ornt /_r { sflg {/_t {0 rmoveto}bdef /ron false def} { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse }bdef 1800 11850 _m (For)_S 89 _t (the)_S 88 _t (other)_S 88 _t (two)_S 88 _t (methods,)_S 88 _t (the)_S 88 _t (nonlinear)_S 88 _t (equations)_S 89 _t (problem)_S 88 _t (is)_S 88 _t (converted)_S 88 _t (into)_S 88 _t (a)_S 88 _t (specialized)_S 1200 11650 _m (minimization)_S 59 _t (problem.)_S 116 _t (The)_S 58 _t (usual)_S 58 _t (objective)_S 58 _t (function)_S 58 _t (to)_S 59 _t (be)_S 58 _t (minimized)_S 58 _t (is)_S 58 _t /Times-ItalicR 550 _ff (f)_S /Times-RomanR 550 _ff (=1/2)_S 58 _t /Times-BoldR 550 _ff (F)_S /Times-RomanR 550 _ff (\()_S /Times-BoldR 550 _ff (x)_S /Times-RomanR 550 _ff (\))_S /Times-RomanR 330 _ff 7425 11725 _m (T)_S 7492 11725 _m /Times-BoldR 550 _ff 7492 11650 _m (F)_S /Times-RomanR 550 _ff (\()_S /Times-BoldR 550 _ff (x)_S /Times-RomanR 550 _ff (\))_S 58 _t (but)_S 58 _t (NNES)_S 58 _t (also)_S 1200 11450 _m (has)_S 55 _t (the)_S 55 _t (capability)_S 55 _t (of)_S 54 _t (employing)_S 55 _t (a)_S 55 _t (second)_S 55 _t (objective)_S 55 _t (function)_S 55 _t (\(often)_S 55 _t (called)_S 55 _t (the)_S 54 _t /Times-ItalicR 550 _ff (natural)_S /Times-RomanR 550 _ff 55 _t (objective)_S 55 _t (function\).)_S 1200 11250 _m (Mathematically,)_S 58 _t (the)_S 59 _t (problem)_S 58 _t (is)_S 59 _t (solved)_S 58 _t (when)_S 59 _t (the)_S 58 _t (objective)_S 59 _t (function,)_S 58 _t /Times-ItalicR 550 _ff (f)_S /Times-RomanR 550 _ff (,)_S 59 _t (reaches)_S 58 _t (zero.)_S 117 _t (The)_S 59 _t (method)_S 58 _t (to)_S 59 _t (find)_S 1200 11050 _m (this)_S 58 _t (minimum)_S 57 _t (is)_S 58 _t (different,)_S 58 _t (however,)_S 58 _t (than)_S 57 _t (that)_S 58 _t (which)_S 58 _t (would)_S 57 _t (be)_S 58 _t (used)_S 58 _t (by)_S 57 _t (a)_S 58 _t (general)_S 57 _t (nonlinear)_S 58 _t (minimization)_S 1200 10850 _m (program)_S 63 _t (because)_S 63 _t (of)_S 63 _t (the)_S 63 _t (special)_S 63 _t (structure)_S 64 _t (of)_S 63 _t (the)_S 63 _t (objective)_S 63 _t (function)_S 63 _t (and)_S 63 _t (the)_S 63 _t (knowledge)_S 64 _t (that)_S 63 _t (the)_S 63 _t (objective)_S 1200 10650 _m (has)_S 61 _t (a)_S 61 _t (minimum)_S 61 _t (at)_S 61 _t (zero.)_S 1800 10250 _m (One)_S 53 _t (of)_S 53 _t (two)_S 52 _t (procedures)_S 53 _t (may)_S 53 _t (be)_S 53 _t (used)_S 53 _t (to)_S 52 _t (enhance)_S 53 _t (convergence:)_S 53 _t (a)_S 52 _t (line)_S 53 _t (search)_S 53 _t (in)_S 53 _t (the)_S 53 _t (direction)_S 52 _t (of)_S 53 _t (the)_S 1200 10050 _m (Newton)_S 73 _t (step)_S 73 _t (or)_S 73 _t (a)_S 73 _t (trust)_S 73 _t (region)_S 73 _t (method)_S 73 _t (in)_S 73 _t (which)_S 73 _t (a)_S 73 _t (linear)_S 72 _t (combination)_S 73 _t (of)_S 73 _t (a)_S 73 _t (step)_S 73 _t (in)_S 73 _t (the)_S 73 _t (steepest)_S 73 _t (descent)_S 1200 9850 _m (direction)_S 59 _t (for)_S 60 _t (the)_S 59 _t (objective)_S 59 _t (function)_S 59 _t (and)_S 60 _t (the)_S 59 _t (Newton)_S 59 _t (step)_S 60 _t (is)_S 59 _t (found)_S 59 _t (which)_S 59 _t (produces)_S 60 _t (a)_S 59 _t (step)_S 59 _t (of)_S 60 _t (a)_S 59 _t (designated)_S 1200 9650 _m (length)_S 53 _t (\(the)_S 52 _t (trust)_S 53 _t (region)_S 53 _t (size,)_S 52 _t (DELTA\).)_S 105 _t (Thus)_S 53 _t (the)_S 52 _t (trust)_S 53 _t (region)_S 52 _t (method)_S 53 _t (restricts)_S 53 _t (the)_S 52 _t (step)_S 53 _t (length)_S 52 _t (to)_S 53 _t (be)_S 52 _t (within)_S 1200 9450 _m (a)_S 47 _t (region)_S 48 _t (in)_S 48 _t (which)_S 47 _t (some)_S 48 _t (confidence)_S 47 _t (is)_S 48 _t (held)_S 48 _t (that)_S 47 _t (the)_S 48 _t (quadratic)_S 47 _t (model)_S 48 _t (for)_S 47 _t (the)_S 48 _t (objective)_S 48 _t (function,)_S 47 _t (upon)_S 48 _t (which)_S 1200 9250 _m (the)_S 44 _t (Newton)_S 45 _t (step)_S 44 _t (is)_S 44 _t (based,)_S 45 _t (is)_S 44 _t (a)_S 45 _t (reasonably)_S 44 _t (accurate)_S 44 _t (representation)_S 45 _t (of)_S 44 _t (the)_S 44 _t (actual)_S 45 _t (objective)_S 44 _t (function.)_S 89 _t (The)_S 44 _t (size)_S 1200 9050 _m (of)_S 71 _t (the)_S 71 _t (trust)_S 70 _t (region)_S 71 _t (is)_S 71 _t (adjusted)_S 70 _t (at)_S 71 _t (each)_S 71 _t (step)_S 70 _t (depending)_S 71 _t (on)_S 70 _t (how)_S 71 _t (well)_S 71 _t (the)_S 70 _t (model)_S 71 _t (and)_S 71 _t (the)_S 71 _t (actual)_S 70 _t (objective)_S 1200 8850 _m (function)_S 61 _t (agree.)_S 122 _t (A)_S 61 _t (detailed)_S 61 _t (description)_S 61 _t (of)_S 61 _t (these)_S 61 _t (methods)_S 61 _t (is)_S 61 _t (given)_S 61 _t (in)_S 61 _t (Section)_S 61 _t (3.)_S 1200 8650 _m 61 _t 1800 8450 _m (The)_S 44 _t (Jacobian)_S 44 _t (matrix)_S 45 _t (need)_S 44 _t (not)_S 45 _t (be)_S 44 _t (evaluated)_S 45 _t (explicitly)_S 44 _t (at)_S 44 _t (each)_S 45 _t (iteration)_S 44 _t (as)_S 45 _t (two)_S 44 _t (quasi-Newton)_S 45 _t (update)_S 1200 8250 _m (methods)_S 47 _t (are)_S 47 _t (also)_S 47 _t (available:)_S 47 _t (Broyden's)_S 48 _t (\(1965\))_S 47 _t (method)_S 47 _t (and)_S 47 _t (a)_S 47 _t (more)_S 47 _t (recent)_S 48 _t (method)_S 47 _t (proposed)_S 47 _t (by)_S 47 _t (Lee)_S 47 _t (and)_S 47 _t (Lee)_S 1200 8050 _m (\(1989\).)_S 97 _t (If)_S 49 _t (the)_S 48 _t (Jacobian)_S 49 _t (matrix)_S 48 _t (is)_S 49 _t (to)_S 48 _t (be)_S 49 _t (evaluated)_S 48 _t (explicitly)_S 49 _t (there)_S 48 _t (are)_S 49 _t (two)_S 48 _t (methods,)_S 49 _t (namely)_S 49 _t (a)_S 48 _t (user-supplied)_S 1200 7850 _m (analytical)_S 61 _t (Jacobian)_S 61 _t (or)_S 61 _t (via)_S 61 _t (finite)_S 61 _t (differences.)_S 1800 7450 _m (Within)_S 87 _t (this)_S 87 _t (framework)_S 87 _t (there)_S 87 _t (are)_S 87 _t (many)_S 87 _t (other)_S 87 _t (options)_S 87 _t (which)_S 87 _t (are)_S 87 _t (set)_S 87 _t (to)_S 86 _t (default)_S 87 _t (values)_S 87 _t (by)_S 87 _t (the)_S 1200 7250 _m (subroutine)_S 61 _t (SETUP)_S 61 _t (which)_S 61 _t (has)_S 61 _t (the)_S 61 _t (following)_S 61 _t (argument)_S 61 _t (list:)_S /CourierR 500 _ff 1800 6850 _m (SUBROUTINE)_S 100 _t (SETUP\(ABSNEW)_S 100 _t (,CAUCHY)_S 100 _t (,DEUFLH)_S 100 _t (,GEOMS)_S 200 _t (,LINESR)_S 100 _t (,)_S 3000 6650 _m 100 _t 100 _t 100 _t 100 _t 100 _t (NEWTON)_S 100 _t (,OVERCH)_S 100 _t (,ACPTCR)_S 100 _t (,ITSCLF)_S 100 _t (,ITSCLX)_S 100 _t (,)_S 3000 6450 _m 100 _t 100 _t 100 _t 100 _t 100 _t (JACTYP)_S 100 _t (,JUPDM)_S 200 _t (,MAXEXP)_S 100 _t (,MAXIT)_S 200 _t (,MAXNS)_S 200 _t (,)_S 3000 6250 _m 100 _t 100 _t 100 _t 100 _t 100 _t (MAXQNS)_S 100 _t (,MINQNS)_S 100 _t (,N)_S 600 _t (,NARMIJ)_S 100 _t (,NIEJEV)_S 100 _t (,)_S 3000 6050 _m 100 _t 100 _t 100 _t 100 _t 100 _t (NJACCH)_S 100 _t (,OUTPUT)_S 100 _t (,QNUPDM)_S 100 _t (,STOPCR)_S 100 _t (,SUPPRS)_S 100 _t (,)_S 3000 5850 _m 100 _t 100 _t 100 _t 100 _t 100 _t (TRUPDM)_S 100 _t (,ALPHA)_S 200 _t (,CONFAC)_S 100 _t (,DELTA)_S 200 _t (,DELFAC)_S 100 _t (,)_S 3000 5650 _m 100 _t 100 _t 100 _t 100 _t 100 _t (EPSMCH)_S 100 _t (,ETAFAC)_S 100 _t (,FDTOLJ)_S 100 _t (,FTOL)_S 300 _t (,LAM0)_S 300 _t (,)_S 3000 5450 _m 100 _t 100 _t 100 _t 100 _t 100 _t (MSTPF)_S 200 _t (,NSTTOL)_S 100 _t (,OMEGA)_S 200 _t (,RATIOF)_S 100 _t (,SIGMA)_S 200 _t (,)_S 3000 5250 _m 100 _t 100 _t 100 _t 100 _t 100 _t (STPTOL)_S 100 _t (,BOUNDL)_S 100 _t (,BOUNDU)_S 100 _t (,SCALEF)_S 100 _t (,SCALEX)_S 100 _t (,)_S 3000 5050 _m 100 _t 100 _t 100 _t 100 _t 100 _t (HELP)_S 300 _t (\))_S /Times-RomanR 550 _ff 1800 4650 _m (In)_S 51 _t (this)_S 51 _t (subroutine,)_S 51 _t (as)_S 51 _t (is)_S 51 _t (the)_S 51 _t (case)_S 51 _t (for)_S 51 _t (all)_S 51 _t (subroutines)_S 51 _t (in)_S 51 _t (NNES,)_S 51 _t (arguments)_S 50 _t (are)_S 51 _t (given)_S 51 _t (in)_S 51 _t (alphabetical)_S 1200 4450 _m (order)_S 54 _t (within)_S 55 _t (each)_S 54 _t (classification)_S 55 _t (of)_S 54 _t (LOGICAL,)_S 54 _t (INTEGER,)_S 55 _t (DOUBLE)_S 54 _t (PRECISION)_S 55 _t (NUMBER,)_S 54 _t (DOUBLE)_S 1200 4250 _m (PRECISION)_S 90 _t (MATRIX)_S 89 _t (\(includes)_S 89 _t (vectors\))_S 89 _t (and)_S 90 _t (CHARACTER.)_S 178 _t (Note)_S 90 _t (that)_S 89 _t (first-letter)_S 89 _t (conventions)_S 89 _t (for)_S 1200 4050 _m (integers)_S 61 _t (are)_S 61 _t (not)_S 61 _t (followed,)_S 61 _t (e.g.,)_S 61 _t (ACPTCR)_S 61 _t (is)_S 61 _t (the)_S 61 _t (first)_S 61 _t (INTEGER.)_S 1800 3850 _m (Because)_S 71 _t (more)_S 71 _t (than)_S 71 _t (one)_S 71 _t (method)_S 71 _t (is)_S 71 _t (included)_S 71 _t (in)_S 71 _t (NNES,)_S 71 _t (there)_S 71 _t (is)_S 71 _t (a)_S 71 _t (hierarchy)_S 71 _t (of)_S 71 _t (options)_S 71 _t (which)_S 71 _t (is)_S 1200 3650 _m (shown)_S 48 _t (in)_S 47 _t (Table)_S 48 _t (1.)_S 95 _t (The)_S 48 _t (first)_S 47 _t (section)_S 48 _t (shows)_S 47 _t (how)_S 48 _t (the)_S 48 _t (three)_S 47 _t (key)_S 48 _t (logical)_S 47 _t (variables,)_S 48 _t (NEWTON,)_S 47 _t (ABSNEW)_S 48 _t (and)_S 1200 3450 _m (LINESR,)_S 49 _t (must)_S 48 _t (be)_S 48 _t (set)_S 49 _t (to)_S 48 _t (obtain)_S 48 _t (the)_S 49 _t (desired)_S 48 _t (method.)_S 97 _t (The)_S 48 _t (default)_S 48 _t (values)_S 49 _t (are)_S 48 _t (designated)_S 48 _t (with)_S 49 _t (asterisks.)_S 96 _t (The)_S 1200 3250 _m (second)_S 55 _t (section)_S 55 _t (lists)_S 55 _t (the)_S 55 _t (options)_S 55 _t (which)_S 55 _t (are)_S 56 _t (available)_S 55 _t (for)_S 55 _t (each)_S 55 _t (method.)_S 110 _t (Not)_S 55 _t (included)_S 55 _t (in)_S 55 _t (the)_S 55 _t (table)_S 56 _t (are)_S 55 _t (those)_S 1200 3050 _m (variables)_S 87 _t (which)_S 86 _t (govern)_S 86 _t (output)_S 86 _t (only,)_S 86 _t (namely)_S 86 _t (OUTPUT)_S 86 _t (and)_S 86 _t (SUPPRS,)_S 86 _t (and)_S 86 _t (those)_S 86 _t (variables)_S 86 _t (which)_S 86 _t (are)_S 1200 2850 _m (common)_S 58 _t (to)_S 57 _t (each)_S 57 _t (method:)_S 57 _t (OVERCH;)_S 58 _t (JACTYP;)_S 57 _t (JUPDM;)_S 57 _t (MAXEXP;)_S 57 _t (MAXIT;)_S 58 _t (N;)_S 57 _t (NJACCH;)_S 57 _t (QNUPDM;)_S 1200 2650 _m (STOPCR;)_S 61 _t (TRMCOD;)_S 61 _t (FTOL;)_S 61 _t (NSTTOL;)_S 61 _t (OMEGA)_S 61 _t (and)_S 61 _t (STPTOL.)_S 1200 2450 _m 61 _t 61 _t 1800 2450 _m (There)_S 93 _t (are)_S 93 _t (also)_S 93 _t (variables)_S 92 _t (which)_S 93 _t (are)_S 93 _t (required)_S 93 _t (for)_S 92 _t (special)_S 93 _t (situations)_S 93 _t (only.)_S 185 _t (These)_S 93 _t (are)_S 93 _t (held)_S 92 _t (in)_S 1200 2250 _m (COMMON)_S 113 _t (blocks:)_S 112 _t (MATSUP;)_S 112 _t (WRNSUP;)_S 113 _t (BYPASS)_S 112 _t (and)_S 113 _t (NFETOT,)_S 112 _t (the)_S 112 _t (total)_S 113 _t (number)_S 112 _t (of)_S 112 _t (function)_S 1200 2050 _m (evaluations.)_S 122 _t (These)_S 61 _t (are)_S 61 _t (also)_S 61 _t (common)_S 61 _t (to)_S 61 _t (each)_S 61 _t (method.)_S 4932 1250 _m (-)_S 61 _t (4)_S 61 _t (-)_S _ep _bp /Times-RomanR 550 _ff 0 13200 10200 _ornt /_r { sflg {/_t {0 rmoveto}bdef /ron false def} { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse }bdef gsave 0 0 translate 4 4 scale _s 1 _w _s 100 _gs 787 2997 _m _sp 1076 2997 1076 3001 787 3001 3 _pl _f _s _s 100 _gs 787 2932 _m _sp 791 2932 791 3001 787 3001 3 _pl _f _s 64 284 791 2932 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1075 2997 _m _sp 1394 2997 1394 3001 1075 3001 3 _pl _f _s _s 100 _gs 1075 2932 _m _sp 1079 2932 1079 3001 1075 3001 3 _pl _f _s 64 314 1079 2932 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1393 2997 _m _sp 1822 2997 1822 3001 1393 3001 3 _pl _f _s 64 428 1393 2932 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 2932 _m _sp 2250 2932 2250 3001 2246 3001 3 _pl _f _s _s 100 _gs 1821 2997 _m _sp 2250 2997 2250 3001 1821 3001 3 _pl _f _s 64 424 1821 2932 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 787 2817 _m _sp 791 2817 791 2932 787 2932 3 _pl _f _s 114 284 791 2817 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1075 2817 _m _sp 1079 2817 1079 2932 1075 2932 3 _pl _f _s 114 314 1079 2817 _cw _s 3300 2550 674 801 _cw _s grestore 5673 11514 _m 61 _t 61 _t 61 _t 61 _t 61 _t (METHOD)_S 427 _t 6340 11314 _m 61 _t 61 _t 61 _t gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 2817 _m _sp 2250 2817 2250 2932 2246 2932 3 _pl _f _s 114 424 1821 2817 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 787 2813 _m _sp 1076 2813 1076 2817 787 2817 3 _pl _f _s _s 100 _gs 787 2748 _m _sp 791 2748 791 2817 787 2817 3 _pl _f _s 64 284 791 2748 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1075 2813 _m _sp 1394 2813 1394 2817 1075 2817 3 _pl _f _s _s 100 _gs 1075 2748 _m _sp 1079 2748 1079 2817 1075 2817 3 _pl _f _s 64 314 1079 2748 _cw _s 3300 2550 674 801 _cw _s grestore 4468 11038 _m (ABSOLUTE)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 1393 2813 _m _sp 1822 2813 1822 2817 1393 2817 3 _pl _f _s _s 100 _gs 1393 2748 _m _sp 1397 2748 1397 2817 1393 2817 3 _pl _f _s 64 424 1397 2748 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 2748 _m _sp 2250 2748 2250 2817 2246 2817 3 _pl _f _s _s 100 _gs 1821 2813 _m _sp 2250 2813 2250 2817 1821 2817 3 _pl _f _s _s 100 _gs 1821 2748 _m _sp 1825 2748 1825 2817 1821 2817 3 _pl _f _s 64 420 1825 2748 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 787 2633 _m _sp 791 2633 791 2748 787 2748 3 _pl _f _s 114 284 791 2633 _cw _s 3300 2550 674 801 _cw _s grestore 3337 10778 _m (NEWTON)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 1075 2633 _m _sp 1079 2633 1079 2748 1075 2748 3 _pl _f _s 114 314 1079 2633 _cw _s 3300 2550 674 801 _cw _s grestore 4550 10778 _m (NEWTON)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 1393 2633 _m _sp 1397 2633 1397 2748 1393 2748 3 _pl _f _s 114 424 1397 2633 _cw _s 3300 2550 674 801 _cw _s grestore 5686 10778 _m 61 _t 61 _t (LINE)_S 61 _t (SEARCH)_S 183 _t 6348 10578 _m 61 _t 61 _t 61 _t gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 2633 _m _sp 2250 2633 2250 2748 2246 2748 3 _pl _f _s _s 100 _gs 1821 2633 _m _sp 1825 2633 1825 2748 1821 2748 3 _pl _f _s 114 420 1825 2633 _cw _s 3300 2550 674 801 _cw _s grestore 7476 10778 _m (TRUST)_S 61 _t (REGION)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 2629 _m _sp 788 2629 788 2633 300 2633 3 _pl _f _s _s 100 _gs 300 2564 _m _sp 304 2564 304 2633 300 2633 3 _pl _f _s 64 483 304 2564 _cw _s 3300 2550 674 801 _cw _s grestore 1786 10302 _m (NEWTON)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 787 2629 _m _sp 1076 2629 1076 2633 787 2633 3 _pl _f _s _s 100 _gs 787 2564 _m _sp 791 2564 791 2633 787 2633 3 _pl _f _s 64 284 791 2564 _cw _s 3300 2550 674 801 _cw _s grestore 3495 10302 _m (TRUE)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 1075 2629 _m _sp 1394 2629 1394 2633 1075 2633 3 _pl _f _s _s 100 _gs 1075 2564 _m _sp 1079 2564 1079 2633 1075 2633 3 _pl _f _s 64 314 1079 2564 _cw _s 3300 2550 674 801 _cw _s grestore 4667 10302 _m (FALSE)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 1393 2629 _m _sp 1822 2629 1822 2633 1393 2633 3 _pl _f _s _s 100 _gs 1393 2564 _m _sp 1397 2564 1397 2633 1393 2633 3 _pl _f _s 64 424 1397 2564 _cw _s 3300 2550 674 801 _cw _s grestore 6113 10302 _m (FALSE*)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 2564 _m _sp 2250 2564 2250 2633 2246 2633 3 _pl _f _s _s 100 _gs 1821 2629 _m _sp 2250 2629 2250 2633 1821 2633 3 _pl _f _s _s 100 _gs 1821 2564 _m _sp 1825 2564 1825 2633 1821 2633 3 _pl _f _s 64 420 1825 2564 _cw _s 3300 2550 674 801 _cw _s grestore 7863 10302 _m (FALSE)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 2560 _m _sp 788 2560 788 2564 300 2564 3 _pl _f _s _s 100 _gs 300 2495 _m _sp 304 2495 304 2564 300 2564 3 _pl _f _s 64 483 304 2495 _cw _s 3300 2550 674 801 _cw _s grestore 1796 10026 _m (ABSNEW)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 787 2560 _m _sp 1076 2560 1076 2564 787 2564 3 _pl _f _s _s 100 _gs 787 2495 _m _sp 791 2495 791 2564 787 2564 3 _pl _f _s 64 284 791 2495 _cw _s 3300 2550 674 801 _cw _s grestore 3454 10026 _m (FALSE)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 1075 2560 _m _sp 1394 2560 1394 2564 1075 2564 3 _pl _f _s _s 100 _gs 1075 2495 _m _sp 1079 2495 1079 2564 1075 2564 3 _pl _f _s 64 314 1079 2495 _cw _s 3300 2550 674 801 _cw _s grestore 4708 10026 _m (TRUE)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 1393 2560 _m _sp 1822 2560 1822 2564 1393 2564 3 _pl _f _s _s 100 _gs 1393 2495 _m _sp 1397 2495 1397 2564 1393 2564 3 _pl _f _s 64 424 1397 2495 _cw _s 3300 2550 674 801 _cw _s grestore 6113 10026 _m (FALSE*)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 2495 _m _sp 2250 2495 2250 2564 2246 2564 3 _pl _f _s _s 100 _gs 1821 2560 _m _sp 2250 2560 2250 2564 1821 2564 3 _pl _f _s _s 100 _gs 1821 2495 _m _sp 1825 2495 1825 2564 1821 2564 3 _pl _f _s 64 420 1825 2495 _cw _s 3300 2550 674 801 _cw _s grestore 7863 10026 _m (FALSE)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 2491 _m _sp 788 2491 788 2495 300 2495 3 _pl _f _s _s 100 _gs 300 2426 _m _sp 304 2426 304 2495 300 2495 3 _pl _f _s 64 483 304 2426 _cw _s 3300 2550 674 801 _cw _s grestore 1862 9750 _m (LINESR)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 787 2491 _m _sp 1076 2491 1076 2495 787 2495 3 _pl _f _s _s 100 _gs 787 2426 _m _sp 791 2426 791 2495 787 2495 3 _pl _f _s 64 284 791 2426 _cw _s 3300 2550 674 801 _cw _s grestore 3495 9750 _m (TRUE)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 1075 2491 _m _sp 1394 2491 1394 2495 1075 2495 3 _pl _f _s _s 100 _gs 1075 2426 _m _sp 1079 2426 1079 2495 1075 2495 3 _pl _f _s 64 314 1079 2426 _cw _s 3300 2550 674 801 _cw _s grestore 4708 9750 _m (TRUE)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 1393 2491 _m _sp 1822 2491 1822 2495 1393 2495 3 _pl _f _s _s 100 _gs 1393 2426 _m _sp 1397 2426 1397 2495 1393 2495 3 _pl _f _s 64 424 1397 2426 _cw _s 3300 2550 674 801 _cw _s grestore 6123 9750 _m 61 _t (TRUE*)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 2426 _m _sp 2250 2426 2250 2495 2246 2495 3 _pl _f _s _s 100 _gs 1821 2491 _m _sp 2250 2491 2250 2495 1821 2495 3 _pl _f _s _s 100 _gs 1821 2426 _m _sp 1825 2426 1825 2495 1821 2495 3 _pl _f _s 64 420 1825 2426 _cw _s 3300 2550 674 801 _cw _s grestore 7863 9750 _m (FALSE)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 2422 _m _sp 788 2422 788 2426 300 2426 3 _pl _f _s _s 100 _gs 300 2357 _m _sp 304 2357 304 2426 300 2426 3 _pl _f _s 64 483 304 2357 _cw _s 3300 2550 674 801 _cw _s grestore 1893 9474 _m (Options)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 787 2422 _m _sp 1076 2422 1076 2426 787 2426 3 _pl _f _s _s 100 _gs 787 2357 _m _sp 791 2357 791 2426 787 2426 3 _pl _f _s 64 284 791 2357 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1075 2422 _m _sp 1394 2422 1394 2426 1075 2426 3 _pl _f _s _s 100 _gs 1075 2357 _m _sp 1079 2357 1079 2426 1075 2426 3 _pl _f _s 64 314 1079 2357 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1393 2422 _m _sp 1822 2422 1822 2426 1393 2426 3 _pl _f _s _s 100 _gs 1393 2357 _m _sp 1397 2357 1397 2426 1393 2426 3 _pl _f _s 64 424 1397 2357 _cw _s 3300 2550 674 801 _cw _s grestore 6078 9474 _m (DEUFLH)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 2357 _m _sp 2250 2357 2250 2426 2246 2426 3 _pl _f _s _s 100 _gs 1821 2422 _m _sp 2250 2422 2250 2426 1821 2426 3 _pl _f _s _s 100 _gs 1821 2357 _m _sp 1825 2357 1825 2426 1821 2426 3 _pl _f _s 64 420 1825 2357 _cw _s 3300 2550 674 801 _cw _s grestore 7756 9474 _m (CAUCHY)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 2292 _m _sp 304 2292 304 2357 300 2357 3 _pl _f _s 64 483 304 2292 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 787 2292 _m _sp 791 2292 791 2357 787 2357 3 _pl _f _s 64 284 791 2292 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1075 2292 _m _sp 1079 2292 1079 2357 1075 2357 3 _pl _f _s 64 314 1079 2292 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1393 2292 _m _sp 1397 2292 1397 2357 1393 2357 3 _pl _f _s 64 424 1397 2292 _cw _s 3300 2550 674 801 _cw _s grestore 6118 9214 _m (GEOMS)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 2292 _m _sp 2250 2292 2250 2357 2246 2357 3 _pl _f _s _s 100 _gs 1821 2292 _m _sp 1825 2292 1825 2357 1821 2357 3 _pl _f _s 64 420 1825 2292 _cw _s 3300 2550 674 801 _cw _s grestore 7786 9214 _m (ACPTCR)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 2227 _m _sp 304 2227 304 2292 300 2292 3 _pl _f _s 64 483 304 2227 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 787 2227 _m _sp 791 2227 791 2292 787 2292 3 _pl _f _s 64 284 791 2227 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1075 2227 _m _sp 1079 2227 1079 2292 1075 2292 3 _pl _f _s 64 314 1079 2227 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1393 2227 _m _sp 1397 2227 1397 2292 1393 2292 3 _pl _f _s 64 424 1397 2227 _cw _s 3300 2550 674 801 _cw _s grestore 6082 8954 _m (ACPTCR)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 2227 _m _sp 2250 2227 2250 2292 2246 2292 3 _pl _f _s _s 100 _gs 1821 2227 _m _sp 1825 2227 1825 2292 1821 2292 3 _pl _f _s 64 420 1825 2227 _cw _s 3300 2550 674 801 _cw _s grestore 7837 8954 _m (ITSCLF)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 2162 _m _sp 304 2162 304 2227 300 2227 3 _pl _f _s 64 483 304 2162 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 787 2162 _m _sp 791 2162 791 2227 787 2227 3 _pl _f _s 64 284 791 2162 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1075 2162 _m _sp 1079 2162 1079 2227 1075 2227 3 _pl _f _s 64 314 1079 2162 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1393 2162 _m _sp 1397 2162 1397 2227 1393 2227 3 _pl _f _s 64 424 1397 2162 _cw _s 3300 2550 674 801 _cw _s grestore 6133 8694 _m (ITSCLF)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 2162 _m _sp 2250 2162 2250 2227 2246 2227 3 _pl _f _s _s 100 _gs 1821 2162 _m _sp 1825 2162 1825 2227 1821 2227 3 _pl _f _s 64 420 1825 2162 _cw _s 3300 2550 674 801 _cw _s grestore 7822 8694 _m (ITSCLX)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 2097 _m _sp 304 2097 304 2162 300 2162 3 _pl _f _s 64 483 304 2097 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 787 2097 _m _sp 791 2097 791 2162 787 2162 3 _pl _f _s 64 284 791 2097 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1075 2097 _m _sp 1079 2097 1079 2162 1075 2162 3 _pl _f _s 64 314 1079 2097 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1393 2097 _m _sp 1397 2097 1397 2162 1393 2162 3 _pl _f _s 64 424 1397 2097 _cw _s 3300 2550 674 801 _cw _s grestore 6118 8434 _m (ITSCLX)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 2097 _m _sp 2250 2097 2250 2162 2246 2162 3 _pl _f _s _s 100 _gs 1821 2097 _m _sp 1825 2097 1825 2162 1821 2162 3 _pl _f _s 64 420 1825 2097 _cw _s 3300 2550 674 801 _cw _s grestore 7812 8434 _m (MAXNS)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 2032 _m _sp 304 2032 304 2097 300 2097 3 _pl _f _s 64 483 304 2032 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 787 2032 _m _sp 791 2032 791 2097 787 2097 3 _pl _f _s 64 284 791 2032 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1075 2032 _m _sp 1079 2032 1079 2097 1075 2097 3 _pl _f _s 64 314 1079 2032 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1393 2032 _m _sp 1397 2032 1397 2097 1393 2097 3 _pl _f _s 64 424 1397 2032 _cw _s 3300 2550 674 801 _cw _s grestore 6108 8174 _m (MAXNS)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 2032 _m _sp 2250 2032 2250 2097 2246 2097 3 _pl _f _s _s 100 _gs 1821 2032 _m _sp 1825 2032 1825 2097 1821 2097 3 _pl _f _s 64 420 1825 2032 _cw _s 3300 2550 674 801 _cw _s grestore 7746 8174 _m (MAXQNS)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 1967 _m _sp 304 1967 304 2032 300 2032 3 _pl _f _s 64 483 304 1967 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 787 1967 _m _sp 791 1967 791 2032 787 2032 3 _pl _f _s 64 284 791 1967 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1075 1967 _m _sp 1079 1967 1079 2032 1075 2032 3 _pl _f _s 64 314 1079 1967 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1393 1967 _m _sp 1397 1967 1397 2032 1393 2032 3 _pl _f _s 64 424 1397 1967 _cw _s 3300 2550 674 801 _cw _s grestore 6042 7914 _m (MAXQNS)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 1967 _m _sp 2250 1967 2250 2032 2246 2032 3 _pl _f _s _s 100 _gs 1821 1967 _m _sp 1825 1967 1825 2032 1821 2032 3 _pl _f _s 64 420 1825 1967 _cw _s 3300 2550 674 801 _cw _s grestore 7782 7914 _m (MINQNS)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 1902 _m _sp 304 1902 304 1967 300 1967 3 _pl _f _s 64 483 304 1902 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 787 1902 _m _sp 791 1902 791 1967 787 1967 3 _pl _f _s 64 284 791 1902 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1075 1902 _m _sp 1079 1902 1079 1967 1075 1967 3 _pl _f _s 64 314 1079 1902 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1393 1902 _m _sp 1397 1902 1397 1967 1393 1967 3 _pl _f _s 64 424 1397 1902 _cw _s 3300 2550 674 801 _cw _s grestore 6078 7654 _m (MINQNS)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 1902 _m _sp 2250 1902 2250 1967 2246 1967 3 _pl _f _s _s 100 _gs 1821 1902 _m _sp 1825 1902 1825 1967 1821 1967 3 _pl _f _s 64 420 1825 1902 _cw _s 3300 2550 674 801 _cw _s grestore 7802 7654 _m (NARMIJ)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 1837 _m _sp 304 1837 304 1902 300 1902 3 _pl _f _s 64 483 304 1837 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 787 1837 _m _sp 791 1837 791 1902 787 1902 3 _pl _f _s 64 284 791 1837 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1075 1837 _m _sp 1079 1837 1079 1902 1075 1902 3 _pl _f _s 64 314 1079 1837 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1393 1837 _m _sp 1397 1837 1397 1902 1393 1902 3 _pl _f _s 64 424 1397 1837 _cw _s 3300 2550 674 801 _cw _s grestore 6098 7394 _m (NARMIJ)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 1837 _m _sp 2250 1837 2250 1902 2246 1902 3 _pl _f _s _s 100 _gs 1821 1837 _m _sp 1825 1837 1825 1902 1821 1902 3 _pl _f _s 64 420 1825 1837 _cw _s 3300 2550 674 801 _cw _s grestore 7832 7394 _m (NIEJEV)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 1772 _m _sp 304 1772 304 1837 300 1837 3 _pl _f _s 64 483 304 1772 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 787 1772 _m _sp 791 1772 791 1837 787 1837 3 _pl _f _s 64 284 791 1772 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1075 1772 _m _sp 1079 1772 1079 1837 1075 1837 3 _pl _f _s 64 314 1079 1772 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1393 1772 _m _sp 1397 1772 1397 1837 1393 1837 3 _pl _f _s 64 424 1397 1772 _cw _s 3300 2550 674 801 _cw _s grestore 6128 7134 _m (NIEJEV)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 1772 _m _sp 2250 1772 2250 1837 2246 1837 3 _pl _f _s _s 100 _gs 1821 1772 _m _sp 1825 1772 1825 1837 1821 1837 3 _pl _f _s 64 420 1825 1772 _cw _s 3300 2550 674 801 _cw _s grestore 7761 7134 _m (TRUPDM)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 1707 _m _sp 304 1707 304 1772 300 1772 3 _pl _f _s 64 483 304 1707 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 787 1707 _m _sp 791 1707 791 1772 787 1772 3 _pl _f _s 64 284 791 1707 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1075 1707 _m _sp 1079 1707 1079 1772 1075 1772 3 _pl _f _s 64 314 1079 1707 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1393 1707 _m _sp 1397 1707 1397 1772 1393 1772 3 _pl _f _s 64 424 1397 1707 _cw _s 3300 2550 674 801 _cw _s grestore 6134 6874 _m (ALPHA)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 1707 _m _sp 2250 1707 2250 1772 2246 1772 3 _pl _f _s _s 100 _gs 1821 1707 _m _sp 1825 1707 1825 1772 1821 1772 3 _pl _f _s 64 420 1825 1707 _cw _s 3300 2550 674 801 _cw _s grestore 7838 6874 _m (ALPHA)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 1642 _m _sp 304 1642 304 1707 300 1707 3 _pl _f _s 64 483 304 1642 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 787 1642 _m _sp 791 1642 791 1707 787 1707 3 _pl _f _s 64 284 791 1642 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1075 1642 _m _sp 1079 1642 1079 1707 1075 1707 3 _pl _f _s 64 314 1079 1642 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1393 1642 _m _sp 1397 1642 1397 1707 1393 1707 3 _pl _f _s 64 424 1397 1642 _cw _s 3300 2550 674 801 _cw _s grestore 6067 6614 _m (CONFAC)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 1642 _m _sp 2250 1642 2250 1707 2246 1707 3 _pl _f _s _s 100 _gs 1821 1642 _m _sp 1825 1642 1825 1707 1821 1707 3 _pl _f _s 64 420 1825 1642 _cw _s 3300 2550 674 801 _cw _s grestore 7771 6614 _m (CONFAC)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 1577 _m _sp 304 1577 304 1642 300 1642 3 _pl _f _s 64 483 304 1577 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 787 1577 _m _sp 791 1577 791 1642 787 1642 3 _pl _f _s 64 284 791 1577 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1075 1577 _m _sp 1079 1577 1079 1642 1075 1642 3 _pl _f _s 64 314 1079 1577 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1393 1577 _m _sp 1397 1577 1397 1642 1393 1642 3 _pl _f _s 64 424 1397 1577 _cw _s 3300 2550 674 801 _cw _s grestore 6159 6354 _m 61 _t (LAM0)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 1577 _m _sp 2250 1577 2250 1642 2246 1642 3 _pl _f _s _s 100 _gs 1821 1577 _m _sp 1825 1577 1825 1642 1821 1642 3 _pl _f _s 64 420 1825 1577 _cw _s 3300 2550 674 801 _cw _s grestore 7843 6354 _m (DELTA)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 1512 _m _sp 304 1512 304 1577 300 1577 3 _pl _f _s 64 483 304 1512 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 787 1512 _m _sp 791 1512 791 1577 787 1577 3 _pl _f _s 64 284 791 1512 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1075 1512 _m _sp 1079 1512 1079 1577 1075 1577 3 _pl _f _s 64 314 1079 1512 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1393 1512 _m _sp 1397 1512 1397 1577 1393 1577 3 _pl _f _s 64 424 1397 1512 _cw _s 3300 2550 674 801 _cw _s grestore 6118 6094 _m 61 _t (MSTPF)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 1512 _m _sp 2250 1512 2250 1577 2246 1577 3 _pl _f _s _s 100 _gs 1821 1512 _m _sp 1825 1512 1825 1577 1821 1577 3 _pl _f _s 64 420 1825 1512 _cw _s 3300 2550 674 801 _cw _s grestore 7787 6094 _m (DELFAC)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 1447 _m _sp 304 1447 304 1512 300 1512 3 _pl _f _s 64 483 304 1447 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 787 1447 _m _sp 791 1447 791 1512 787 1512 3 _pl _f _s 64 284 791 1447 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1075 1447 _m _sp 1079 1447 1079 1512 1075 1512 3 _pl _f _s 64 314 1079 1447 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1393 1447 _m _sp 1397 1447 1397 1512 1393 1512 3 _pl _f _s 64 424 1397 1447 _cw _s 3300 2550 674 801 _cw _s grestore 6108 5834 _m (RATIOF)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 1447 _m _sp 2250 1447 2250 1512 2246 1512 3 _pl _f _s _s 100 _gs 1821 1447 _m _sp 1825 1447 1825 1512 1821 1512 3 _pl _f _s 64 420 1825 1447 _cw _s 3300 2550 674 801 _cw _s grestore 7787 5834 _m (ETAFAC)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 1382 _m _sp 304 1382 304 1447 300 1447 3 _pl _f _s 64 483 304 1382 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 787 1382 _m _sp 791 1382 791 1447 787 1447 3 _pl _f _s 64 284 791 1382 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1075 1382 _m _sp 1079 1382 1079 1447 1075 1447 3 _pl _f _s 64 314 1079 1382 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1393 1382 _m _sp 1397 1382 1397 1447 1393 1447 3 _pl _f _s 64 424 1397 1382 _cw _s 3300 2550 674 801 _cw _s grestore 6144 5574 _m (SIGMA)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 1382 _m _sp 2250 1382 2250 1447 2246 1447 3 _pl _f _s _s 100 _gs 1821 1382 _m _sp 1825 1382 1825 1447 1821 1447 3 _pl _f _s 64 420 1825 1382 _cw _s 3300 2550 674 801 _cw _s grestore 7853 5574 _m (MSTPF)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 1317 _m _sp 304 1317 304 1382 300 1382 3 _pl _f _s 64 483 304 1317 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 787 1317 _m _sp 791 1317 791 1382 787 1382 3 _pl _f _s 64 284 791 1317 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1075 1317 _m _sp 1079 1317 1079 1382 1075 1382 3 _pl _f _s 64 314 1079 1317 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1393 1317 _m _sp 1397 1317 1397 1382 1393 1382 3 _pl _f _s 64 424 1397 1317 _cw _s 3300 2550 674 801 _cw _s grestore 6057 5314 _m (BOUNDL)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 1317 _m _sp 2250 1317 2250 1382 2246 1382 3 _pl _f _s _s 100 _gs 1821 1317 _m _sp 1825 1317 1825 1382 1821 1382 3 _pl _f _s 64 420 1825 1317 _cw _s 3300 2550 674 801 _cw _s grestore 7812 5314 _m (RATIOF)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 1252 _m _sp 304 1252 304 1317 300 1317 3 _pl _f _s 64 483 304 1252 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 787 1252 _m _sp 791 1252 791 1317 787 1317 3 _pl _f _s 64 284 791 1252 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1075 1252 _m _sp 1079 1252 1079 1317 1075 1317 3 _pl _f _s 64 314 1079 1252 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1393 1252 _m _sp 1397 1252 1397 1317 1393 1317 3 _pl _f _s 64 424 1397 1252 _cw _s 3300 2550 674 801 _cw _s grestore 6047 5054 _m (BOUNDU)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 1252 _m _sp 2250 1252 2250 1317 2246 1317 3 _pl _f _s _s 100 _gs 1821 1252 _m _sp 1825 1252 1825 1317 1821 1317 3 _pl _f _s 64 420 1825 1252 _cw _s 3300 2550 674 801 _cw _s grestore 7848 5054 _m (SIGMA)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 1187 _m _sp 304 1187 304 1252 300 1252 3 _pl _f _s 64 483 304 1187 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 787 1187 _m _sp 791 1187 791 1252 787 1252 3 _pl _f _s 64 284 791 1187 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1075 1187 _m _sp 1079 1187 1079 1252 1075 1252 3 _pl _f _s 64 314 1079 1187 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1393 1187 _m _sp 1397 1187 1397 1252 1393 1252 3 _pl _f _s 64 424 1397 1187 _cw _s 3300 2550 674 801 _cw _s grestore 6098 4794 _m (SCALEF)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 1187 _m _sp 2250 1187 2250 1252 2246 1252 3 _pl _f _s _s 100 _gs 1821 1187 _m _sp 1825 1187 1825 1252 1821 1252 3 _pl _f _s 64 420 1825 1187 _cw _s 3300 2550 674 801 _cw _s grestore 7761 4794 _m (BOUNDL)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 1122 _m _sp 304 1122 304 1187 300 1187 3 _pl _f _s 64 483 304 1122 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 787 1122 _m _sp 791 1122 791 1187 787 1187 3 _pl _f _s 64 284 791 1122 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1075 1122 _m _sp 1079 1122 1079 1187 1075 1187 3 _pl _f _s 64 314 1079 1122 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1393 1122 _m _sp 1397 1122 1397 1187 1393 1187 3 _pl _f _s 64 424 1397 1122 _cw _s 3300 2550 674 801 _cw _s grestore 6083 4534 _m (SCALEX)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 1122 _m _sp 2250 1122 2250 1187 2246 1187 3 _pl _f _s _s 100 _gs 1821 1122 _m _sp 1825 1122 1825 1187 1821 1187 3 _pl _f _s 64 420 1825 1122 _cw _s 3300 2550 674 801 _cw _s grestore 7751 4534 _m (BOUNDU)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 1057 _m _sp 304 1057 304 1122 300 1122 3 _pl _f _s 64 483 304 1057 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 787 1057 _m _sp 791 1057 791 1122 787 1122 3 _pl _f _s 64 284 791 1057 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1075 1057 _m _sp 1079 1057 1079 1122 1075 1122 3 _pl _f _s 64 314 1079 1057 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1393 1057 _m _sp 1397 1057 1397 1122 1393 1122 3 _pl _f _s 64 424 1397 1057 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 1057 _m _sp 2250 1057 2250 1122 2246 1122 3 _pl _f _s _s 100 _gs 1821 1057 _m _sp 1825 1057 1825 1122 1821 1122 3 _pl _f _s 64 420 1825 1057 _cw _s 3300 2550 674 801 _cw _s grestore 7802 4274 _m (SCALEF)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 988 _m _sp 788 988 788 992 300 992 3 _pl _f _s _s 100 _gs 300 988 _m _sp 304 988 304 1057 300 1057 3 _pl _f _s 64 483 304 992 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 787 988 _m _sp 1076 988 1076 992 787 992 3 _pl _f _s _s 100 _gs 787 988 _m _sp 791 988 791 1057 787 1057 3 _pl _f _s 64 284 791 992 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1075 988 _m _sp 1394 988 1394 992 1075 992 3 _pl _f _s _s 100 _gs 1075 988 _m _sp 1079 988 1079 1057 1075 1057 3 _pl _f _s 64 314 1079 992 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1393 988 _m _sp 1822 988 1822 992 1393 992 3 _pl _f _s _s 100 _gs 1393 988 _m _sp 1397 988 1397 1057 1393 1057 3 _pl _f _s 64 424 1397 992 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1821 988 _m _sp 2250 988 2250 992 1821 992 3 _pl _f _s _s 100 _gs 2246 988 _m _sp 2250 988 2250 1057 2246 1057 3 _pl _f _s _s 100 _gs 1821 988 _m _sp 1825 988 1825 1057 1821 1057 3 _pl _f _s 64 420 1825 992 _cw _s 3300 2550 674 801 _cw _s grestore 7787 4014 _m (SCALEX)_S 3115 3598 _m (Table)_S 61 _t (1)_S 122 _t (Required)_S 61 _t (and)_S 61 _t (Optional)_S 61 _t (Variables)_S 61 _t (for)_S 61 _t (NNES)_S 4046 3398 _m (*)_S 61 _t (designates)_S 61 _t (default)_S 61 _t (settings)_S 1800 2998 _m (If)_S 62 _t (incompatible)_S 61 _t (options)_S 62 _t (are)_S 61 _t (used,)_S 62 _t (a)_S 61 _t (warning)_S 62 _t (will)_S 61 _t (be)_S 61 _t (issued)_S 62 _t (by)_S 61 _t (NNES)_S 62 _t (and)_S 61 _t (execution)_S 62 _t (will)_S 61 _t (usually)_S 1200 2798 _m (continue)_S 61 _t (with)_S 61 _t (the)_S 61 _t (options)_S 61 _t (used)_S 61 _t (being)_S 61 _t (declared)_S 61 _t (by)_S 61 _t (NNES.)_S 1800 2598 _m (Each)_S 50 _t (option)_S 50 _t (is)_S 49 _t (briefly)_S 50 _t (described)_S 50 _t (in)_S 50 _t (Table)_S 50 _t (2.)_S 99 _t (If)_S 50 _t (changes)_S 50 _t (are)_S 50 _t (desired,)_S 50 _t (these)_S 50 _t (must)_S 49 _t (be)_S 50 _t (set)_S 50 _t (between)_S 50 _t (the)_S 1200 2398 _m (calls)_S 61 _t (to)_S 61 _t (SETUP)_S 61 _t (and)_S 61 _t (NNES.)_S 122 _t (The)_S 61 _t (possible)_S 61 _t (values)_S 61 _t (are)_S 61 _t (given)_S 61 _t (within)_S 61 _t (each)_S 61 _t (description.)_S 1800 2198 _m (Because)_S 71 _t (of)_S 72 _t (the)_S 71 _t (large)_S 71 _t (number)_S 72 _t (of)_S 71 _t (options)_S 71 _t (the)_S 71 _t (sensitivity)_S 72 _t (of)_S 71 _t (the)_S 72 _t (program)_S 71 _t (to)_S 71 _t (changes)_S 71 _t (in)_S 72 _t (the)_S 71 _t (input)_S 1200 1998 _m (parameters)_S 67 _t (is)_S 67 _t (discussed)_S 67 _t (following)_S 67 _t (Table)_S 67 _t (2.)_S 135 _t (Also)_S 67 _t (given)_S 67 _t (are)_S 67 _t (some)_S 67 _t (suggestions)_S 67 _t (on)_S 67 _t (how)_S 67 _t (problems)_S 67 _t (can)_S 68 _t (be)_S 1200 1798 _m (transformed)_S 61 _t (for)_S 61 _t (easier)_S 61 _t (solution.)_S 122 _t 4932 1250 _m (-)_S 61 _t (5)_S 61 _t (-)_S _ep _bp /Times-RomanR 550 _ff 0 13200 10200 _ornt /_r { sflg {/_t {0 rmoveto}bdef /ron false def} { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse }bdef gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 2997 _m _sp 610 2997 610 3001 300 3001 3 _pl _f _s _s 100 _gs 300 2917 _m _sp 304 2917 304 3001 300 3001 3 _pl _f _s 79 305 304 2917 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 609 2997 _m _sp 1971 2997 1971 3001 609 3001 3 _pl _f _s _s 100 _gs 609 2917 _m _sp 613 2917 613 3001 609 3001 3 _pl _f _s 79 1357 613 2917 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 2917 _m _sp 2250 2917 2250 3001 2246 3001 3 _pl _f _s _s 100 _gs 1970 2997 _m _sp 2250 2997 2250 3001 1970 3001 3 _pl _f _s _s 100 _gs 1970 2917 _m _sp 1974 2917 1974 3001 1970 3001 3 _pl _f _s 79 271 1974 2917 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 2837 _m _sp 304 2837 304 2917 300 2917 3 _pl _f _s 79 305 304 2837 _cw _s 3300 2550 674 801 _cw _s grestore 1414 11394 _m (VARIABLE)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 609 2837 _m _sp 613 2837 613 2917 609 2917 3 _pl _f _s 79 1357 613 2837 _cw _s 3300 2550 674 801 _cw _s grestore 4621 11394 _m (DESCRIPTION)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 2837 _m _sp 2250 2837 2250 2917 2246 2917 3 _pl _f _s _s 100 _gs 1970 2837 _m _sp 1974 2837 1974 2917 1970 2917 3 _pl _f _s 79 271 1974 2837 _cw _s 3300 2550 674 801 _cw _s grestore 8072 11394 _m (DEFAULT)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 606 2757 _m _sp 610 2757 610 2837 606 2837 3 _pl _f _s _s 100 _gs 300 2757 _m _sp 304 2757 304 2837 300 2837 3 _pl _f _s 79 301 304 2757 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 609 2757 _m _sp 613 2757 613 2837 609 2837 3 _pl _f _s 79 1357 613 2757 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 2757 _m _sp 2250 2757 2250 2837 2246 2837 3 _pl _f _s _s 100 _gs 1970 2757 _m _sp 1974 2757 1974 2837 1970 2837 3 _pl _f _s 79 271 1974 2757 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 2753 _m _sp 610 2753 610 2757 300 2757 3 _pl _f _s _s 100 _gs 300 2523 _m _sp 304 2523 304 2757 300 2757 3 _pl _f _s 229 305 304 2523 _cw _s 3300 2550 674 801 _cw _s grestore 1490 10738 _m (ABSNEW)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 609 2753 _m _sp 1971 2753 1971 2757 609 2757 3 _pl _f _s _s 100 _gs 609 2523 _m _sp 613 2523 613 2757 609 2757 3 _pl _f _s 229 1357 613 2523 _cw _s 3300 2550 674 801 _cw _s grestore 2554 10738 _m (Switches)_S 61 _t (to)_S 61 _t (Absolute)_S 61 _t (Newton's)_S 61 _t (method;)_S 61 _t (NEWTON)_S 61 _t (should)_S 61 _t (be)_S 61 _t (FALSE)_S 2554 10538 _m (and)_S 61 _t (LINESR)_S 61 _t (should)_S 61 _t (be)_S 61 _t (TRUE.)_S 122 _t (\(If)_S 61 _t (both)_S 61 _t (NEWTON)_S 61 _t (and)_S 61 _t (ABSNEW)_S 2554 10338 _m (are)_S 61 _t (TRUE)_S 61 _t (the)_S 61 _t (Absolute)_S 61 _t (Newton's)_S 61 _t (method)_S 61 _t (is)_S 61 _t (used)_S 61 _t (and)_S 61 _t (a)_S 61 _t (warning)_S 2554 10138 _m (issued\).)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 2523 _m _sp 2250 2523 2250 2757 2246 2757 3 _pl _f _s _s 100 _gs 1970 2753 _m _sp 2250 2753 2250 2757 1970 2757 3 _pl _f _s _s 100 _gs 1970 2523 _m _sp 1974 2523 1974 2757 1970 2757 3 _pl _f _s 229 271 1974 2523 _cw _s 3300 2550 674 801 _cw _s grestore 8210 10738 _m (FALSE)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 2519 _m _sp 610 2519 610 2523 300 2523 3 _pl _f _s _s 100 _gs 300 2089 _m _sp 304 2089 304 2523 300 2523 3 _pl _f _s 429 305 304 2089 _cw _s 3300 2550 674 801 _cw _s grestore 1531 9802 _m (BYPASS)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 609 2519 _m _sp 1971 2519 1971 2523 609 2523 3 _pl _f _s _s 100 _gs 609 2089 _m _sp 613 2089 613 2523 609 2523 3 _pl _f _s 429 1357 613 2089 _cw _s 3300 2550 674 801 _cw _s grestore 2554 9802 _m (Bypasses)_S 61 _t (calculation)_S 61 _t (of)_S 61 _t (condition)_S 61 _t (number)_S 61 _t (and)_S 61 _t (the)_S 61 _t (remedial)_S 61 _t (measures)_S 2554 9602 _m (of)_S 61 _t (Dennis)_S 61 _t (and)_S 61 _t (Schnabel)_S 61 _t (\(1983\))_S 61 _t (for)_S 61 _t (ill-conditioned)_S 61 _t (Jacobians.)_S 61 _t 2554 9402 _m (Execution)_S 61 _t (always)_S 61 _t (continues)_S 61 _t (as)_S 61 _t (if)_S 61 _t (Jacobian)_S 61 _t (were)_S 61 _t (well-conditioned)_S 2554 9202 _m (\(unless)_S 61 _t (it)_S 61 _t (is)_S 61 _t (found)_S 61 _t (to)_S 61 _t (be)_S 61 _t (singular\).)_S 122 _t (Switching)_S 61 _t (BYPASS)_S 61 _t (to)_S 61 _t (TRUE)_S 61 _t (may)_S 2554 9002 _m (be)_S 61 _t (useful)_S 61 _t (in)_S 61 _t (two)_S 61 _t (ways:)_S 61 _t (to)_S 61 _t (save)_S 61 _t (time)_S 61 _t (if)_S 61 _t (you)_S 61 _t (know)_S 61 _t (the)_S 61 _t (system)_S 61 _t (is)_S 61 _t (well-)_S 2554 8802 _m (conditioned)_S 61 _t (and)_S 61 _t (don't)_S 61 _t (need)_S 61 _t (the)_S 61 _t (condition)_S 61 _t (number)_S 61 _t (estimation)_S 61 _t (or)_S 61 _t (if)_S 61 _t (you)_S 2554 8602 _m (would)_S 61 _t (prefer)_S 61 _t (the)_S 61 _t (possibly)_S 61 _t (inaccurate)_S 61 _t (Newton)_S 61 _t (step)_S 61 _t (from)_S 61 _t (a)_S 61 _t (ill-)_S 2554 8402 _m (conditioned)_S 61 _t (system.)_S 61 _t gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 2089 _m _sp 2250 2089 2250 2523 2246 2523 3 _pl _f _s _s 100 _gs 1970 2519 _m _sp 2250 2519 2250 2523 1970 2523 3 _pl _f _s _s 100 _gs 1970 2089 _m _sp 1974 2089 1974 2523 1970 2523 3 _pl _f _s 429 271 1974 2089 _cw _s 3300 2550 674 801 _cw _s grestore 8210 9802 _m (FALSE)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 2085 _m _sp 610 2085 610 2089 300 2089 3 _pl _f _s _s 100 _gs 300 1605 _m _sp 304 1605 304 2089 300 2089 3 _pl _f _s 479 305 304 1605 _cw _s 3300 2550 674 801 _cw _s grestore 1490 8066 _m (CAUCHY)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 609 2085 _m _sp 1971 2085 1971 2089 609 2089 3 _pl _f _s _s 100 _gs 609 1605 _m _sp 613 1605 613 2089 609 2089 3 _pl _f _s 479 1357 613 1605 _cw _s 3300 2550 674 801 _cw _s grestore 2554 8066 _m (The)_S 61 _t (initial)_S 61 _t (trust)_S 61 _t (region)_S 61 _t (size,)_S 61 _t (DELTA,)_S 61 _t (may)_S 61 _t (be)_S 61 _t (set)_S 61 _t (by)_S 61 _t (the)_S 61 _t (user)_S 61 _t (or)_S 61 _t (by)_S 61 _t (the)_S 2554 7866 _m (program.)_S 122 _t (If)_S 61 _t (the)_S 61 _t (program)_S 61 _t (is)_S 61 _t (used,)_S 61 _t (DELTA)_S 61 _t (is)_S 61 _t (set)_S 61 _t (to)_S 61 _t (the)_S 61 _t (length)_S 61 _t (of)_S 61 _t (the)_S 2554 7666 _m (initial)_S 61 _t (Newton)_S 61 _t (step)_S 61 _t (\(CAUCHY)_S 61 _t (is)_S 61 _t (FALSE\))_S 61 _t (or)_S 61 _t (to)_S 61 _t (the)_S 61 _t (distance)_S 61 _t (to)_S 61 _t (the)_S 2554 7466 _m (minimum)_S 61 _t (of)_S 61 _t (the)_S 61 _t (quadratic)_S 61 _t (model)_S 61 _t (of)_S 61 _t (the)_S 61 _t (objective)_S 61 _t (function)_S 61 _t (in)_S 61 _t (the)_S 2554 7266 _m (steepest)_S 61 _t (descent)_S 61 _t (direction,)_S 61 _t (the)_S 61 _t (Cauchy)_S 61 _t (point)_S 61 _t (\(CAUCHY)_S 61 _t (is)_S 61 _t (TRUE\).)_S 61 _t 2554 7066 _m (DELTA)_S 61 _t (must)_S 61 _t (be)_S 61 _t /Symbol 550 _ff (\243)_S /Times-RomanR 550 _ff 61 _t (0)_S 61 _t (on)_S 61 _t (entry)_S 61 _t (for)_S 61 _t (either)_S 61 _t (of)_S 61 _t (these)_S 61 _t (two)_S 61 _t (methods)_S 61 _t (to)_S 61 _t (be)_S 2554 6866 _m (used.)_S 122 _t (The)_S 61 _t (Newton)_S 61 _t (length)_S 61 _t (is)_S 61 _t (always)_S 61 _t (greater,)_S 61 _t (thus)_S 61 _t (setting)_S 61 _t (CAUCHY)_S 61 _t (to)_S 2554 6666 _m (TRUE)_S 61 _t (is,)_S 61 _t (generally,)_S 61 _t (a)_S 61 _t (more)_S 61 _t (conservative)_S 61 _t (and)_S 61 _t (thus)_S 61 _t (a)_S 61 _t (slower)_S 61 _t (approach.)_S 122 _t 2554 6466 _m 61 _t gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 1605 _m _sp 2250 1605 2250 2089 2246 2089 3 _pl _f _s _s 100 _gs 1970 2085 _m _sp 2250 2085 2250 2089 1970 2089 3 _pl _f _s _s 100 _gs 1970 1605 _m _sp 1974 1605 1974 2089 1970 2089 3 _pl _f _s 479 271 1974 1605 _cw _s 3300 2550 674 801 _cw _s grestore 8210 8066 _m (FALSE)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 1601 _m _sp 610 1601 610 1605 300 1605 3 _pl _f _s _s 100 _gs 300 1321 _m _sp 304 1321 304 1605 300 1605 3 _pl _f _s 279 305 304 1321 _cw _s 3300 2550 674 801 _cw _s grestore 1516 6130 _m (DEUFLH)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 609 1601 _m _sp 1971 1601 1971 1605 609 1605 3 _pl _f _s _s 100 _gs 609 1321 _m _sp 613 1321 613 1605 609 1605 3 _pl _f _s 279 1357 613 1321 _cw _s 3300 2550 674 801 _cw _s grestore 2554 6130 _m (The)_S 61 _t (initial)_S 61 _t (line)_S 61 _t (search)_S 61 _t (relaxation)_S 61 _t (factor,)_S 61 _t /Symbol 550 _ff (l)_S /Times-RomanR 550 _ff (,)_S 61 _t (can)_S 61 _t (be)_S 61 _t (set)_S 61 _t (to)_S 61 _t (LAM0)_S 61 _t (or)_S 61 _t (by)_S 2554 5930 _m (a)_S 61 _t (version)_S 61 _t (of)_S 61 _t (Deuflhard's)_S 61 _t (\(1974,1975\))_S 61 _t (relaxation)_S 61 _t (factor)_S 61 _t (initialization)_S 2554 5730 _m (process)_S 61 _t (which)_S 61 _t (estimates)_S 61 _t (what)_S 61 _t (the)_S 61 _t (relaxation)_S 61 _t (factor)_S 61 _t (should)_S 61 _t (be)_S 61 _t (at)_S 61 _t (each)_S 2554 5530 _m (iteration.)_S 122 _t (LAM0)_S 61 _t (is)_S 61 _t (usually)_S 61 _t (1.0)_S 61 _t (but)_S 61 _t (may)_S 61 _t (be)_S 61 _t (made)_S 61 _t (smaller)_S 61 _t (if)_S 61 _t (the)_S 2554 5330 _m (problem)_S 61 _t (is)_S 61 _t (extremely)_S 61 _t (nonlinear.)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 1321 _m _sp 2250 1321 2250 1605 2246 1605 3 _pl _f _s _s 100 _gs 1970 1601 _m _sp 2250 1601 2250 1605 1970 1605 3 _pl _f _s _s 100 _gs 1970 1321 _m _sp 1974 1321 1974 1605 1970 1605 3 _pl _f _s 279 271 1974 1321 _cw _s 3300 2550 674 801 _cw _s grestore 8220 6130 _m 61 _t (TRUE)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 1317 _m _sp 610 1317 610 1321 300 1321 3 _pl _f _s _s 100 _gs 300 737 _m _sp 304 737 304 1321 300 1321 3 _pl _f _s 579 305 304 737 _cw _s 3300 2550 674 801 _cw _s grestore 1556 4994 _m (GEOMS)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 609 1317 _m _sp 1971 1317 1971 1321 609 1321 3 _pl _f _s _s 100 _gs 609 737 _m _sp 613 737 613 1321 609 1321 3 _pl _f _s 579 1357 613 737 _cw _s 3300 2550 674 801 _cw _s grestore 2554 4994 _m (Two)_S 61 _t (types)_S 61 _t (of)_S 61 _t (search)_S 61 _t (may)_S 61 _t (be)_S 61 _t (used)_S 61 _t (to)_S 61 _t (reduce)_S 61 _t (either)_S 61 _t /Symbol 550 _ff (l)_S /Times-RomanR 550 _ff 61 _t (or)_S 61 _t /Symbol 550 _ff (d)_S /Times-RomanR 550 _ff (.)_S 122 _t (In)_S 61 _t (the)_S 2554 4794 _m (geometric)_S 61 _t (search)_S 61 _t (the)_S 61 _t (length)_S 61 _t (is)_S 61 _t (decreased)_S 61 _t (at)_S 61 _t (each)_S 61 _t (stage)_S 61 _t (by)_S 61 _t (multiplying)_S 2554 4594 _m (the)_S 61 _t (current)_S 61 _t /Symbol 550 _ff (l)_S /Times-RomanR 550 _ff (,)_S 61 _t (by)_S 61 _t (the)_S 61 _t (factor)_S 61 _t (SIGMA)_S 61 _t (\(usually)_S 61 _t (0.5\))_S 61 _t (or)_S 61 _t (dividing)_S 61 _t /Symbol 550 _ff (d)_S /Times-RomanR 550 _ff 61 _t (by)_S 2554 4394 _m (DELFAC)_S 61 _t (\(usually)_S 61 _t (2.0\).)_S 61 _t (If)_S 61 _t (GEOMS)_S 61 _t (is)_S 61 _t (FALSE)_S 61 _t (then)_S 61 _t (for)_S 61 _t (line)_S 61 _t (searches)_S 61 _t (at)_S 2554 4194 _m (the)_S 61 _t (first)_S 61 _t (stage)_S 61 _t (and)_S 61 _t (trust)_S 61 _t (region)_S 61 _t (steps)_S 61 _t (for)_S 61 _t (all)_S 61 _t (stages,)_S 61 _t (a)_S 61 _t (quadratic)_S 61 _t (function)_S 2554 3994 _m (of)_S 61 _t (the)_S 61 _t (relaxation)_S 61 _t (factor)_S 61 _t (or)_S 61 _t (DELTA,)_S 61 _t (respectively,)_S 61 _t (is)_S 61 _t (minimized)_S 61 _t (using)_S 2554 3794 _m (the)_S 61 _t (initial)_S 61 _t (objective)_S 61 _t (function)_S 61 _t (value,)_S 61 _t (the)_S 61 _t (trial)_S 61 _t (point)_S 61 _t (objective)_S 61 _t (function)_S 2554 3594 _m (value)_S 61 _t (and)_S 61 _t (the)_S 61 _t (directional)_S 61 _t (derivative.)_S 122 _t (For)_S 61 _t (line)_S 61 _t (searches,)_S 61 _t (if)_S 61 _t (further)_S 2554 3394 _m (cutbacks)_S 61 _t (are)_S 61 _t (needed,)_S 61 _t (a)_S 61 _t (cubic)_S 61 _t (minimization)_S 61 _t (using)_S 61 _t (the)_S 61 _t (two)_S 61 _t (most)_S 61 _t (recent)_S 2554 3194 _m (objective)_S 61 _t (function)_S 61 _t (values,)_S 61 _t (the)_S 61 _t (initial)_S 61 _t (objective)_S 61 _t (function)_S 61 _t (value)_S 61 _t (and)_S 61 _t (the)_S 2554 2994 _m (directional)_S 61 _t (derivative)_S 61 _t (is)_S 61 _t (used.)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 737 _m _sp 2250 737 2250 1321 2246 1321 3 _pl _f _s _s 100 _gs 1970 1317 _m _sp 2250 1317 2250 1321 1970 1321 3 _pl _f _s _s 100 _gs 1970 737 _m _sp 1974 737 1974 1321 1970 1321 3 _pl _f _s 579 271 1974 737 _cw _s 3300 2550 674 801 _cw _s grestore 8129 4994 _m 61 _t 61 _t (TRUE)_S 122 _t gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 733 _m _sp 610 733 610 737 300 737 3 _pl _f _s _s 100 _gs 300 553 _m _sp 304 553 304 737 300 737 3 _pl _f _s 179 305 304 553 _cw _s 3300 2550 674 801 _cw _s grestore 1556 2658 _m (LINESR)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 609 733 _m _sp 1971 733 1971 737 609 737 3 _pl _f _s _s 100 _gs 609 553 _m _sp 613 553 613 737 609 737 3 _pl _f _s 179 1357 613 553 _cw _s 3300 2550 674 801 _cw _s grestore 2554 2658 _m (Designates)_S 61 _t (whether)_S 61 _t (a)_S 61 _t (line)_S 61 _t (search)_S 61 _t (\(TRUE\))_S 61 _t (or)_S 61 _t (trust)_S 61 _t (region)_S 61 _t (method)_S 2554 2458 _m (\(FALSE\))_S 61 _t (is)_S 61 _t (to)_S 61 _t (be)_S 61 _t (used.)_S 122 _t (Should)_S 61 _t (be)_S 61 _t (TRUE)_S 61 _t (for)_S 61 _t (Newton's)_S 61 _t (or)_S 61 _t (Absolute)_S 2554 2258 _m (Newton's)_S 61 _t (method.)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 553 _m _sp 2250 553 2250 737 2246 737 3 _pl _f _s _s 100 _gs 1970 733 _m _sp 2250 733 2250 737 1970 737 3 _pl _f _s _s 100 _gs 1970 553 _m _sp 1974 553 1974 737 1970 737 3 _pl _f _s 179 271 1974 553 _cw _s 3300 2550 674 801 _cw _s grestore 8220 2658 _m 61 _t (TRUE)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 549 _m _sp 610 549 610 553 300 553 3 _pl _f _s _s 100 _gs 300 469 _m _sp 304 469 304 553 300 553 3 _pl _f _s 79 305 304 469 _cw _s 3300 2550 674 801 _cw _s grestore 1505 1922 _m (MATSUP)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 609 549 _m _sp 1971 549 1971 553 609 553 3 _pl _f _s _s 100 _gs 609 469 _m _sp 613 469 613 553 609 553 3 _pl _f _s 79 1357 613 469 _cw _s 3300 2550 674 801 _cw _s grestore 2554 1922 _m (Suppresses)_S 61 _t (matrix)_S 61 _t (printing)_S 61 _t (in)_S 61 _t (detailed)_S 61 _t (outputs.)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 469 _m _sp 2250 469 2250 553 2246 553 3 _pl _f _s _s 100 _gs 1970 549 _m _sp 2250 549 2250 553 1970 553 3 _pl _f _s _s 100 _gs 1970 469 _m _sp 1974 469 1974 553 1970 553 3 _pl _f _s 79 271 1974 469 _cw _s 3300 2550 674 801 _cw _s grestore 8210 1922 _m (FALSE)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 465 _m _sp 610 465 610 469 300 469 3 _pl _f _s _s 100 _gs 300 465 _m _sp 304 465 304 469 300 469 3 _pl _f _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 609 465 _m _sp 1971 465 1971 469 609 469 3 _pl _f _s _s 100 _gs 609 465 _m _sp 613 465 613 469 609 469 3 _pl _f _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1970 465 _m _sp 2250 465 2250 469 1970 469 3 _pl _f _s _s 100 _gs 2246 465 _m _sp 2250 465 2250 469 2246 469 3 _pl _f _s _s 100 _gs 1970 465 _m _sp 1974 465 1974 469 1970 469 3 _pl _f _s grestore 4932 1250 _m (-)_S 61 _t (6)_S 61 _t (-)_S _ep _bp /Times-RomanR 550 _ff 0 13200 10200 _ornt /_r { sflg {/_t {0 rmoveto}bdef /ron false def} { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse }bdef gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 2997 _m _sp 610 2997 610 3001 300 3001 3 _pl _f _s _s 100 _gs 300 2667 _m _sp 304 2667 304 3001 300 3001 3 _pl _f _s 329 305 304 2667 _cw _s 3300 2550 674 801 _cw _s grestore 1480 11714 _m (NEWTON)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 609 2997 _m _sp 1971 2997 1971 3001 609 3001 3 _pl _f _s _s 100 _gs 609 2667 _m _sp 613 2667 613 3001 609 3001 3 _pl _f _s 329 1357 613 2667 _cw _s 3300 2550 674 801 _cw _s grestore 2554 11714 _m (Designates)_S 61 _t (that)_S 61 _t (a)_S 61 _t (strict)_S 61 _t (Newton)_S 61 _t (or)_S 61 _t (quasi-Newton)_S 61 _t (method)_S 61 _t (is)_S 61 _t (to)_S 61 _t (be)_S 61 _t (used)_S 2554 11514 _m (if)_S 61 _t (set)_S 61 _t (to)_S 61 _t (TRUE.)_S 122 _t (Otherwise,)_S 61 _t (Absolute)_S 61 _t (Newton's)_S 61 _t (method)_S 61 _t (or)_S 61 _t (either)_S 61 _t (a)_S 2554 11314 _m (line)_S 61 _t (search)_S 61 _t (or)_S 61 _t (a)_S 61 _t (trust)_S 61 _t (region)_S 61 _t (method)_S 61 _t (will)_S 61 _t (be)_S 61 _t (used.)_S 122 _t (LINESR)_S 61 _t (should)_S 2554 11114 _m (also)_S 61 _t (be)_S 61 _t (TRUE)_S 61 _t (if)_S 61 _t (NEWTON)_S 61 _t (is)_S 61 _t (TRUE)_S 61 _t (\(LINESR)_S 61 _t (will)_S 61 _t (be)_S 61 _t (switched)_S 2554 10914 _m (internally)_S 61 _t (if)_S 61 _t (not\).)_S 122 _t (See)_S 61 _t (also)_S 61 _t (JUPDM)_S 61 _t (to)_S 61 _t (choose)_S 61 _t (among)_S 61 _t (Newton)_S 61 _t (or)_S 2554 10714 _m (either)_S 61 _t (quasi-Newton)_S 61 _t (method.)_S 122 _t gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 2667 _m _sp 2250 2667 2250 3001 2246 3001 3 _pl _f _s _s 100 _gs 1970 2997 _m _sp 2250 2997 2250 3001 1970 3001 3 _pl _f _s _s 100 _gs 1970 2667 _m _sp 1974 2667 1974 3001 1970 3001 3 _pl _f _s 329 271 1974 2667 _cw _s 3300 2550 674 801 _cw _s grestore 8210 11714 _m (FALSE)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 2663 _m _sp 610 2663 610 2667 300 2667 3 _pl _f _s _s 100 _gs 300 2433 _m _sp 304 2433 304 2667 300 2667 3 _pl _f _s 229 305 304 2433 _cw _s 3300 2550 674 801 _cw _s grestore 1500 10378 _m (OVERCH)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 609 2663 _m _sp 1971 2663 1971 2667 609 2667 3 _pl _f _s _s 100 _gs 609 2433 _m _sp 613 2433 613 2667 609 2667 3 _pl _f _s 229 1357 613 2433 _cw _s 3300 2550 674 801 _cw _s grestore 2554 10378 _m (A)_S 61 _t (check)_S 61 _t (can)_S 61 _t (be)_S 61 _t (made)_S 61 _t (for)_S 61 _t (potential)_S 61 _t (overflows)_S 61 _t (at)_S 61 _t (certain)_S 61 _t (locations)_S 2554 10178 _m (within)_S 61 _t (NNES.)_S 122 _t (If)_S 61 _t (a)_S 61 _t (potential)_S 61 _t (overflow)_S 61 _t (is)_S 61 _t (detected,)_S 61 _t (10)_S /Times-RomanR 395 _ff 6565 10178 _m 6565 10253 _m (MAXEXP)_S 7121 10253 _m /Times-RomanR 550 _ff 7121 10178 _m 61 _t (is)_S 2554 9978 _m (inserted)_S 61 _t (in)_S 61 _t (place.)_S 122 _t (This)_S 61 _t (may)_S 61 _t (prevent)_S 61 _t (a)_S 61 _t (few)_S 61 _t (unnecessary)_S 61 _t (failures)_S 2554 9778 _m (because)_S 61 _t (of)_S 61 _t (overflows.)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 2433 _m _sp 2250 2433 2250 2667 2246 2667 3 _pl _f _s _s 100 _gs 1970 2663 _m _sp 2250 2663 2250 2667 1970 2667 3 _pl _f _s _s 100 _gs 1970 2433 _m _sp 1974 2433 1974 2667 1970 2667 3 _pl _f _s 229 271 1974 2433 _cw _s 3300 2550 674 801 _cw _s grestore 8210 10378 _m (FALSE)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 2429 _m _sp 610 2429 610 2433 300 2433 3 _pl _f _s _s 100 _gs 300 2299 _m _sp 304 2299 304 2433 300 2433 3 _pl _f _s 129 305 304 2299 _cw _s 3300 2550 674 801 _cw _s grestore 1495 9442 _m (WRNSUP)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 609 2429 _m _sp 1971 2429 1971 2433 609 2433 3 _pl _f _s _s 100 _gs 609 2299 _m _sp 613 2299 613 2433 609 2433 3 _pl _f _s 129 1357 613 2299 _cw _s 3300 2550 674 801 _cw _s grestore 2554 9442 _m (Suppresses)_S 61 _t (printing)_S 61 _t (of)_S 61 _t (warnings.)_S 122 _t (Used)_S 61 _t (only)_S 61 _t (if)_S 61 _t (known)_S 61 _t (warnings)_S 61 _t (will)_S 2554 9242 _m (clutter)_S 61 _t (output.)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 2299 _m _sp 2250 2299 2250 2433 2246 2433 3 _pl _f _s _s 100 _gs 1970 2429 _m _sp 2250 2429 2250 2433 1970 2433 3 _pl _f _s _s 100 _gs 1970 2299 _m _sp 1974 2299 1974 2433 1970 2433 3 _pl _f _s 129 271 1974 2299 _cw _s 3300 2550 674 801 _cw _s grestore 8210 9442 _m (FALSE)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 2295 _m _sp 610 2295 610 2299 300 2299 3 _pl _f _s _s 100 _gs 300 2065 _m _sp 304 2065 304 2299 300 2299 3 _pl _f _s 229 305 304 2065 _cw _s 3300 2550 674 801 _cw _s grestore 1520 8906 _m (ACPTCR)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 609 2295 _m _sp 1971 2295 1971 2299 609 2299 3 _pl _f _s _s 100 _gs 609 2065 _m _sp 613 2065 613 2299 609 2299 3 _pl _f _s 229 1357 613 2065 _cw _s 3300 2550 674 801 _cw _s grestore 2554 8906 _m (Denotes)_S 61 _t (whether)_S 61 _t (a)_S 61 _t (step)_S 61 _t (may)_S 61 _t (be)_S 61 _t (accepted)_S 61 _t (based)_S 61 _t (on)_S 61 _t (only)_S 61 _t (the)_S 61 _t (usual)_S 2554 8706 _m (sum-of-squares)_S 61 _t (function)_S 61 _t (value)_S 61 _t (step)_S 61 _t (acceptance)_S 61 _t (criterion,)_S 61 _t /Times-ItalicR 550 _ff (f)_S /Times-RomanR 550 _ff (,)_S 61 _t (whereupon)_S 2554 8506 _m (ACPTCR=1,)_S 61 _t (or)_S 61 _t (if)_S 61 _t (the)_S 61 _t (function)_S 61 _t (value)_S 61 _t (and)_S 61 _t (the)_S 122 _t (natural)_S 61 _t (objective)_S 2554 8306 _m (function)_S 61 _t (step)_S 61 _t (acceptance)_S 61 _t (criteria)_S 61 _t (are)_S 61 _t (both)_S 61 _t (being)_S 61 _t (used,)_S 61 _t (ACPTCR=12.)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 2065 _m _sp 2250 2065 2250 2299 2246 2299 3 _pl _f _s _s 100 _gs 1970 2295 _m _sp 2250 2295 2250 2299 1970 2299 3 _pl _f _s _s 100 _gs 1970 2065 _m _sp 1974 2065 1974 2299 1970 2299 3 _pl _f _s 229 271 1974 2065 _cw _s 3300 2550 674 801 _cw _s grestore 8246 8906 _m 61 _t 61 _t 61 _t 61 _t (12)_S 61 _t gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 2061 _m _sp 610 2061 610 2065 300 2065 3 _pl _f _s _s 100 _gs 300 1781 _m _sp 304 1781 304 2065 300 2065 3 _pl _f _s 279 305 304 1781 _cw _s 3300 2550 674 801 _cw _s grestore 1571 7970 _m (ITSCLF)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 609 2061 _m _sp 1971 2061 1971 2065 609 2065 3 _pl _f _s _s 100 _gs 609 1781 _m _sp 613 1781 613 2065 609 2065 3 _pl _f _s 279 1357 613 1781 _cw _s 3300 2550 674 801 _cw _s grestore 2554 7970 _m (When)_S 61 _t (set)_S 61 _t (to)_S 61 _t (0)_S 61 _t (it)_S 61 _t (implies)_S 61 _t (no)_S 61 _t (adaptive)_S 61 _t (function)_S 61 _t (scaling)_S 61 _t (to)_S 61 _t (be)_S 61 _t (used.)_S 122 _t (For)_S 2554 7770 _m (any)_S 61 _t (integer)_S 61 _t (greater)_S 61 _t (than)_S 61 _t (0,)_S 61 _t (adaptive)_S 61 _t (scaling)_S 61 _t (begins)_S 61 _t (at)_S 61 _t (that)_S 61 _t (iteration.)_S 61 _t 2554 7570 _m (Scaling)_S 61 _t (factors)_S 61 _t (are)_S 61 _t (updated)_S 61 _t (when)_S 61 _t (the)_S 61 _t (Jacobian)_S 61 _t (is)_S 61 _t (evaluated)_S 61 _t (explicitly.)_S 61 _t 2554 7370 _m (No)_S 61 _t (scaling)_S 61 _t (or)_S 61 _t (user-supplied)_S 61 _t (scaling)_S 61 _t (with)_S 61 _t (no)_S 61 _t (updating)_S 61 _t (usually)_S 61 _t (work)_S 2554 7170 _m (best.)_S 61 _t gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 1781 _m _sp 2250 1781 2250 2065 2246 2065 3 _pl _f _s _s 100 _gs 1970 2061 _m _sp 2250 2061 2250 2065 1970 2065 3 _pl _f _s _s 100 _gs 1970 1781 _m _sp 1974 1781 1974 2065 1970 2065 3 _pl _f _s 279 271 1974 1781 _cw _s 3300 2550 674 801 _cw _s grestore 8292 7970 _m 61 _t 61 _t 61 _t 61 _t 61 _t (0)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 1777 _m _sp 610 1777 610 1781 300 1781 3 _pl _f _s _s 100 _gs 300 1497 _m _sp 304 1497 304 1781 300 1781 3 _pl _f _s 279 305 304 1497 _cw _s 3300 2550 674 801 _cw _s grestore 1556 6834 _m (ITSCLX)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 609 1777 _m _sp 1971 1777 1971 1781 609 1781 3 _pl _f _s _s 100 _gs 609 1497 _m _sp 613 1497 613 1781 609 1781 3 _pl _f _s 279 1357 613 1497 _cw _s 3300 2550 674 801 _cw _s grestore 2554 6834 _m (When)_S 61 _t (set)_S 61 _t (to)_S 61 _t (0)_S 61 _t (it)_S 61 _t (implies)_S 61 _t (no)_S 61 _t (adaptive)_S 61 _t (variable)_S 61 _t (scaling)_S 61 _t (to)_S 61 _t (be)_S 61 _t (used.)_S 122 _t (For)_S 2554 6634 _m (any)_S 61 _t (integer)_S 61 _t (greater)_S 61 _t (than)_S 61 _t (0,)_S 61 _t (adaptive)_S 61 _t (scaling)_S 61 _t (begins)_S 61 _t (at)_S 61 _t (that)_S 61 _t (iteration.)_S 61 _t 2554 6434 _m (Scaling)_S 61 _t (factors)_S 61 _t (are)_S 61 _t (updated)_S 61 _t (when)_S 61 _t (the)_S 61 _t (Jacobian)_S 61 _t (is)_S 61 _t (evaluated)_S 61 _t (explicitly.)_S 61 _t 2554 6234 _m (No)_S 61 _t (scaling)_S 61 _t (or)_S 61 _t (user-supplied)_S 61 _t (scaling)_S 61 _t (with)_S 61 _t (no)_S 61 _t (updating)_S 61 _t (usually)_S 61 _t (work)_S 2554 6034 _m (best.)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 1497 _m _sp 2250 1497 2250 1781 2246 1781 3 _pl _f _s _s 100 _gs 1970 1777 _m _sp 2250 1777 2250 1781 1970 1781 3 _pl _f _s _s 100 _gs 1970 1497 _m _sp 1974 1497 1974 1781 1970 1781 3 _pl _f _s 279 271 1974 1497 _cw _s 3300 2550 674 801 _cw _s grestore 8261 6834 _m 61 _t 61 _t 61 _t 61 _t 61 _t (0)_S 61 _t gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 1493 _m _sp 610 1493 610 1497 300 1497 3 _pl _f _s _s 100 _gs 300 1163 _m _sp 304 1163 304 1497 300 1497 3 _pl _f _s 329 305 304 1163 _cw _s 3300 2550 674 801 _cw _s grestore 1541 5698 _m (JACTYP)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 609 1493 _m _sp 1971 1493 1971 1497 609 1497 3 _pl _f _s _s 100 _gs 609 1163 _m _sp 613 1163 613 1497 609 1497 3 _pl _f _s 329 1357 613 1163 _cw _s 3300 2550 674 801 _cw _s grestore 2554 5698 _m (Denotes)_S 61 _t (how)_S 61 _t (the)_S 61 _t (Jacobian)_S 61 _t (is)_S 61 _t (to)_S 61 _t (be)_S 61 _t (explicitly)_S 61 _t (evaluated)_S 61 _t (\(see)_S 61 _t (JUPDM)_S 2554 5498 _m (for)_S 61 _t (choosing)_S 61 _t (how)_S 61 _t (the)_S 61 _t (Jacobian)_S 61 _t (is)_S 61 _t (updated\):)_S 2554 5298 _m (JACTYP=0)_S 122 _t (Analytical)_S 61 _t (Jacobian)_S 61 _t (provided)_S 1586 _t 2554 5098 _m (JACTYP=1)_S 122 _t (Forward)_S 61 _t (Difference)_S 61 _t (Jacobian)_S 1464 _t 2554 4898 _m (JACTYP=2)_S 122 _t (Backward)_S 61 _t (Difference)_S 61 _t (Jacobian)_S 1098 _t (JACTYP=3)_S 61 _t 2554 4698 _m (Central)_S 61 _t (Difference)_S 61 _t (Jacobian)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 1163 _m _sp 2250 1163 2250 1497 2246 1497 3 _pl _f _s _s 100 _gs 1970 1493 _m _sp 2250 1493 2250 1497 1970 1497 3 _pl _f _s _s 100 _gs 1970 1163 _m _sp 1974 1163 1974 1497 1970 1497 3 _pl _f _s 329 271 1974 1163 _cw _s 3300 2550 674 801 _cw _s grestore 8292 5698 _m 61 _t 61 _t 61 _t 61 _t 61 _t (1)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 1159 _m _sp 610 1159 610 1163 300 1163 3 _pl _f _s _s 100 _gs 300 879 _m _sp 304 879 304 1163 300 1163 3 _pl _f _s 279 305 304 879 _cw _s 3300 2550 674 801 _cw _s grestore 1577 4362 _m (JUPDM)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 609 1159 _m _sp 1971 1159 1971 1163 609 1163 3 _pl _f _s _s 100 _gs 609 879 _m _sp 613 879 613 1163 609 1163 3 _pl _f _s 279 1357 613 879 _cw _s 3300 2550 674 801 _cw _s grestore 2554 4362 _m (Jacobian)_S 61 _t (update)_S 61 _t (method:)_S 2554 4162 _m (JUPDM=0)_S 183 _t (Jacobian)_S 61 _t (calculated)_S 61 _t (at)_S 61 _t (every)_S 61 _t (iteration)_S 61 _t (\(either)_S 61 _t (using)_S 610 _t 2554 3962 _m 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t (analytical)_S 61 _t (derivatives)_S 61 _t (or)_S 61 _t (finite)_S 61 _t (differences\))_S 2554 3762 _m (JUPDM=1)_S 183 _t (Broyden's)_S 61 _t (\(1965\))_S 61 _t (quasi-Newton)_S 61 _t (update)_S 2554 3562 _m (JUPDM=2)_S 183 _t (Lee)_S 61 _t (and)_S 61 _t (Lee's)_S 61 _t (\(1989\))_S 61 _t (quasi-Newton)_S 61 _t (update)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 879 _m _sp 2250 879 2250 1163 2246 1163 3 _pl _f _s _s 100 _gs 1970 1159 _m _sp 2250 1159 2250 1163 1970 1163 3 _pl _f _s _s 100 _gs 1970 879 _m _sp 1974 879 1974 1163 1970 1163 3 _pl _f _s 279 271 1974 879 _cw _s 3300 2550 674 801 _cw _s grestore 8261 4362 _m 61 _t 61 _t 61 _t 61 _t 61 _t (0)_S 61 _t gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 875 _m _sp 610 875 610 879 300 879 3 _pl _f _s _s 100 _gs 300 745 _m _sp 304 745 304 879 300 879 3 _pl _f _s 129 305 304 745 _cw _s 3300 2550 674 801 _cw _s grestore 1490 3226 _m (MAXEXP)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 609 875 _m _sp 1971 875 1971 879 609 879 3 _pl _f _s _s 100 _gs 609 745 _m _sp 613 745 613 879 609 879 3 _pl _f _s 129 1357 613 745 _cw _s 3300 2550 674 801 _cw _s grestore 2554 3226 _m (Maximum)_S 61 _t (exponent)_S 61 _t (allowed)_S 61 _t (\(base)_S 61 _t (ten\).)_S 122 _t (This)_S 61 _t (is)_S 61 _t (found)_S 61 _t (internally)_S 61 _t (using)_S 2554 3026 _m (the)_S 61 _t (subroutine)_S 61 _t (MACHAR)_S 61 _t (along)_S 61 _t (with)_S 61 _t (other)_S 61 _t (machine-specific)_S 61 _t (constants.)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 745 _m _sp 2250 745 2250 879 2246 879 3 _pl _f _s _s 100 _gs 1970 875 _m _sp 2250 875 2250 879 1970 879 3 _pl _f _s _s 100 _gs 1970 745 _m _sp 1974 745 1974 879 1970 879 3 _pl _f _s 129 271 1974 745 _cw _s 3300 2550 674 801 _cw _s grestore 8338 3226 _m 61 _t 61 _t 61 _t 61 _t (-)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 741 _m _sp 610 741 610 745 300 745 3 _pl _f _s _s 100 _gs 300 661 _m _sp 304 661 304 745 300 745 3 _pl _f _s 79 305 304 661 _cw _s 3300 2550 674 801 _cw _s grestore 1577 2690 _m (MAXIT)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 609 741 _m _sp 1971 741 1971 745 609 745 3 _pl _f _s _s 100 _gs 609 661 _m _sp 613 661 613 745 609 745 3 _pl _f _s 79 1357 613 661 _cw _s 3300 2550 674 801 _cw _s grestore 2554 2690 _m (Maximum)_S 61 _t (number)_S 61 _t (of)_S 61 _t (iterations)_S 61 _t (allowed.)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 661 _m _sp 2250 661 2250 745 2246 745 3 _pl _f _s _s 100 _gs 1970 741 _m _sp 2250 741 2250 745 1970 745 3 _pl _f _s _s 100 _gs 1970 661 _m _sp 1974 661 1974 745 1970 745 3 _pl _f _s 79 271 1974 661 _cw _s 3300 2550 674 801 _cw _s grestore 8261 2690 _m 61 _t 61 _t 61 _t (250)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 657 _m _sp 610 657 610 661 300 661 3 _pl _f _s _s 100 _gs 300 477 _m _sp 304 477 304 661 300 661 3 _pl _f _s 179 305 304 477 _cw _s 3300 2550 674 801 _cw _s grestore 1546 2354 _m (MAXNS)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 609 657 _m _sp 1971 657 1971 661 609 661 3 _pl _f _s _s 100 _gs 609 477 _m _sp 613 477 613 661 609 661 3 _pl _f _s 179 1357 613 477 _cw _s 3300 2550 674 801 _cw _s grestore 2554 2354 _m (In)_S 61 _t (any)_S 61 _t (iteration,)_S 61 _t (the)_S 61 _t (maximum)_S 61 _t (number)_S 61 _t (of)_S 61 _t (line)_S 61 _t (search)_S 61 _t (or)_S 61 _t (trust)_S 61 _t (region)_S 2554 2154 _m (steps)_S 61 _t (allowed)_S 61 _t (after)_S 61 _t (an)_S 61 _t (explicit)_S 61 _t (Jacobian)_S 61 _t (update.)_S 122 _t (Used)_S 61 _t (in)_S 61 _t (conjunction)_S 2554 1954 _m (with)_S 61 _t (MAXQNS.)_S 122 _t gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 477 _m _sp 2250 477 2250 661 2246 661 3 _pl _f _s _s 100 _gs 1970 657 _m _sp 2250 657 2250 661 1970 661 3 _pl _f _s _s 100 _gs 1970 477 _m _sp 1974 477 1974 661 1970 661 3 _pl _f _s 179 271 1974 477 _cw _s 3300 2550 674 801 _cw _s grestore 8276 2354 _m 61 _t 61 _t 61 _t 61 _t (50)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 473 _m _sp 610 473 610 477 300 477 3 _pl _f _s _s 100 _gs 300 473 _m _sp 304 473 304 477 300 477 3 _pl _f _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 609 473 _m _sp 1971 473 1971 477 609 477 3 _pl _f _s _s 100 _gs 609 473 _m _sp 613 473 613 477 609 477 3 _pl _f _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1970 473 _m _sp 2250 473 2250 477 1970 477 3 _pl _f _s _s 100 _gs 2246 473 _m _sp 2250 473 2250 477 2246 477 3 _pl _f _s _s 100 _gs 1970 473 _m _sp 1974 473 1974 477 1970 477 3 _pl _f _s grestore 4932 1250 _m (-)_S 61 _t (7)_S 61 _t (-)_S _ep _bp /Times-RomanR 550 _ff 0 13200 10200 _ornt /_r { sflg {/_t {0 rmoveto}bdef /ron false def} { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse }bdef gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 2997 _m _sp 610 2997 610 3001 300 3001 3 _pl _f _s _s 100 _gs 300 2717 _m _sp 304 2717 304 3001 300 3001 3 _pl _f _s 279 305 304 2717 _cw _s 3300 2550 674 801 _cw _s grestore 1480 11714 _m (MAXQNS)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 609 2997 _m _sp 1971 2997 1971 3001 609 3001 3 _pl _f _s _s 100 _gs 609 2717 _m _sp 613 2717 613 3001 609 3001 3 _pl _f _s 279 1357 613 2717 _cw _s 3300 2550 674 801 _cw _s grestore 2554 11714 _m (In)_S 61 _t (any)_S 61 _t (iteration,)_S 61 _t (the)_S 61 _t (maximum)_S 61 _t (number)_S 61 _t (of)_S 61 _t (line)_S 61 _t (search)_S 61 _t (trial)_S 61 _t (or)_S 61 _t (trust)_S 2554 11514 _m (region)_S 61 _t (steps)_S 61 _t (allowed)_S 61 _t (after)_S 61 _t (a)_S 61 _t (quasi-Newton)_S 61 _t (Jacobian)_S 61 _t (update.)_S 122 _t (This)_S 61 _t (is)_S 2554 11314 _m (used)_S 61 _t (to)_S 61 _t (prevent)_S 61 _t (an)_S 61 _t (excessive)_S 61 _t (number)_S 61 _t (of)_S 61 _t (trial)_S 61 _t (steps)_S 61 _t (being)_S 61 _t (tried)_S 61 _t (in)_S 61 _t (a)_S 2554 11114 _m (poor)_S 61 _t (search)_S 61 _t (direction)_S 61 _t (because)_S 61 _t (of)_S 61 _t (inaccuracies)_S 61 _t (in)_S 61 _t (the)_S 61 _t (quasi-Newton)_S 2554 10914 _m (Jacobian)_S 61 _t (approximation.)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 2717 _m _sp 2250 2717 2250 3001 2246 3001 3 _pl _f _s _s 100 _gs 1970 2997 _m _sp 2250 2997 2250 3001 1970 3001 3 _pl _f _s _s 100 _gs 1970 2717 _m _sp 1974 2717 1974 3001 1970 3001 3 _pl _f _s 279 271 1974 2717 _cw _s 3300 2550 674 801 _cw _s grestore 8276 11714 _m 61 _t 61 _t 61 _t 61 _t (10)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 2713 _m _sp 610 2713 610 2717 300 2717 3 _pl _f _s _s 100 _gs 300 1905 _m _sp 304 1905 304 2717 300 2717 3 _pl _f _s 807 305 304 1905 _cw _s 3300 2550 674 801 _cw _s grestore 1587 10578 _m 61 _t (MGLL)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 609 2713 _m _sp 1971 2713 1971 2717 609 2717 3 _pl _f _s _s 100 _gs 609 1905 _m _sp 613 1905 613 2717 609 2717 3 _pl _f _s 807 1357 613 1905 _cw _s 3300 2550 674 801 _cw _s grestore 2554 10578 _m (In)_S 61 _t (effect)_S 61 _t (when)_S 61 _t (using)_S 61 _t (the)_S 61 _t (nonmonotonic)_S 61 _t (step)_S 61 _t (acceptance)_S 61 _t (criterion)_S 61 _t (of)_S 2554 10378 _m (Grippo,)_S 61 _t (Lampariello)_S 61 _t (and)_S 61 _t (Lucidi)_S 61 _t (\(1986\),)_S 61 _t (it)_S 61 _t (tells)_S 61 _t (how)_S 61 _t (many)_S 61 _t (previous)_S 2554 10178 _m (values)_S 61 _t (to)_S 61 _t (compare)_S 61 _t (to)_S 61 _t (judge)_S 61 _t (step)_S 61 _t (acceptance.)_S 122 _t (For)_S 61 _t (function)_S 61 _t (value,)_S 61 _t /Times-ItalicR 550 _ff (f)_S /Times-RomanR 550 _ff (,)_S 2554 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F81FFFFFFFFFFFFFFFFFFF041B 992 1351 16 _ieq 8209 1312 1351 24 _ieq E0827F 1584 1351 16 _ieq 0413 992 1350 16 _ieq 8703 1312 1350 16 _ieq E1C0 1584 1350 16 _ieq 0E07 992 1349 16 _ieq 0703 1312 1349 16 _ieq C1C0 1576 1349 24 _ieq FE0E07 992 1348 16 _ieq 0707 1312 1348 16 _ieq C1C1 1576 1348 24 _ieq FE0E0F 1000 1347 8 _ieq 8F 1320 1347 8 _ieq E3 1592 1347 8 _ieq 1F _s grestore gsave 0 0 translate 4 4 scale _s 1 _w _s 100 _gs 2246 1225 _m _sp 2250 1225 2250 1671 2246 1671 3 _pl _f _s _s 100 _gs 1970 1667 _m _sp 2250 1667 2250 1671 1970 1671 3 _pl _f _s _s 100 _gs 1970 1225 _m _sp 1974 1225 1974 1671 1970 1671 3 _pl _f _s 441 271 1974 1225 _cw _s 3300 2550 674 801 _cw _s grestore 8292 6394 _m 61 _t 61 _t 61 _t 61 _t 61 _t (1)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 1221 _m _sp 610 1221 610 1225 300 1225 3 _pl _f _s _s 100 _gs 300 991 _m _sp 304 991 304 1225 300 1225 3 _pl _f _s 229 305 304 991 _cw _s 3300 2550 674 801 _cw _s grestore 1566 4610 _m (NIEJEV)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 609 1221 _m _sp 1971 1221 1971 1225 609 1225 3 _pl _f _s _s 100 _gs 609 991 _m _sp 613 991 613 1225 609 1225 3 _pl _f _s 229 1357 613 991 _cw _s 3300 2550 674 801 _cw _s grestore 2554 4610 _m (Number)_S 61 _t (of)_S 61 _t (initial)_S 61 _t (explicit)_S 61 _t (Jacobian)_S 61 _t (evaluations,)_S 61 _t (i.e.,)_S 61 _t (using)_S 61 _t (an)_S 61 _t (user-)_S 2554 4410 _m (supplied)_S 61 _t (analytical)_S 61 _t (Jacobian)_S 61 _t (or)_S 61 _t (finite-difference)_S 61 _t (approximation.)_S 122 _t (This)_S 2554 4210 _m (delays)_S 61 _t (the)_S 61 _t (start)_S 61 _t (of)_S 61 _t (quasi-Newton)_S 61 _t (steps)_S 61 _t (when)_S 61 _t (the)_S 61 _t (solution)_S 61 _t (is)_S 61 _t (more)_S 2554 4010 _m (sensitive)_S 61 _t (to)_S 61 _t (the)_S 61 _t (initial)_S 61 _t (steps.)_S 122 _t gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 991 _m _sp 2250 991 2250 1225 2246 1225 3 _pl _f _s _s 100 _gs 1970 1221 _m _sp 2250 1221 2250 1225 1970 1225 3 _pl _f _s _s 100 _gs 1970 991 _m _sp 1974 991 1974 1225 1970 1225 3 _pl _f _s 229 271 1974 991 _cw _s 3300 2550 674 801 _cw _s grestore 8292 4610 _m 61 _t 61 _t 61 _t 61 _t 61 _t (1)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 987 _m _sp 610 987 610 991 300 991 3 _pl _f _s _s 100 _gs 300 807 _m _sp 304 807 304 991 300 991 3 _pl _f _s 179 305 304 807 _cw _s 3300 2550 674 801 _cw _s grestore 1521 3674 _m (NJACCH)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 609 987 _m _sp 1971 987 1971 991 609 991 3 _pl _f _s _s 100 _gs 609 807 _m _sp 613 807 613 991 609 991 3 _pl _f _s 179 1357 613 807 _cw _s 3300 2550 674 801 _cw _s grestore 2554 3674 _m (Number)_S 61 _t (of)_S 61 _t (iterations)_S 61 _t (for)_S 61 _t (which)_S 61 _t (the)_S 61 _t (analytical)_S 61 _t (Jacobian)_S 61 _t (is)_S 61 _t (checked)_S 2554 3474 _m (using)_S 61 _t (forward)_S 61 _t (differences)_S 61 _t (if)_S 61 _t (JACTYP=0.)_S 122 _t (See)_S 61 _t (FDTOLJ)_S 61 _t (for)_S 61 _t (a)_S 2554 3274 _m (definition)_S 61 _t (of)_S 61 _t (an)_S 61 _t (acceptable)_S 61 _t (agreement.)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 807 _m _sp 2250 807 2250 991 2246 991 3 _pl _f _s _s 100 _gs 1970 987 _m _sp 2250 987 2250 991 1970 991 3 _pl _f _s _s 100 _gs 1970 807 _m _sp 1974 807 1974 991 1970 991 3 _pl _f _s 179 271 1974 807 _cw _s 3300 2550 674 801 _cw _s grestore 8292 3674 _m 61 _t 61 _t 61 _t 61 _t 61 _t (1)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 803 _m _sp 610 803 610 807 300 807 3 _pl _f _s _s 100 _gs 300 803 _m _sp 304 803 304 807 300 807 3 _pl _f _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 609 803 _m _sp 1971 803 1971 807 609 807 3 _pl _f _s _s 100 _gs 609 803 _m _sp 613 803 613 807 609 807 3 _pl _f _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1970 803 _m _sp 2250 803 2250 807 1970 807 3 _pl _f _s _s 100 _gs 2246 803 _m _sp 2250 803 2250 807 2246 807 3 _pl _f _s _s 100 _gs 1970 803 _m _sp 1974 803 1974 807 1970 807 3 _pl _f _s grestore 4932 1250 _m (-)_S 61 _t (8)_S 61 _t (-)_S _ep _bp /Times-RomanR 550 _ff 0 13200 10200 _ornt /_r { sflg {/_t {0 rmoveto}bdef /ron false def} { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse }bdef gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 2997 _m _sp 610 2997 610 3001 300 3001 3 _pl _f _s _s 100 _gs 300 2567 _m _sp 304 2567 304 3001 300 3001 3 _pl _f _s 429 305 304 2567 _cw _s 3300 2550 674 801 _cw _s grestore 1516 11714 _m (OUTPUT)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 609 2997 _m _sp 1971 2997 1971 3001 609 3001 3 _pl _f _s _s 100 _gs 609 2567 _m _sp 613 2567 613 3001 609 3001 3 _pl _f _s 429 1357 613 2567 _cw _s 3300 2550 674 801 _cw _s grestore 2554 11714 _m (Signifies)_S 61 _t (the)_S 61 _t (level)_S 61 _t (of)_S 61 _t (output.)_S 122 _t (This)_S 61 _t (may)_S 61 _t (be)_S 61 _t (modified)_S 61 _t (by)_S 122 _t (variables)_S 2554 11514 _m (MATSUP,)_S 61 _t (SUPPRS)_S 61 _t (and)_S 61 _t (WRNSUP.)_S 2554 11314 _m (OUTPUT=0)_S 183 _t (no)_S 61 _t (output)_S 2554 11114 _m (OUTPUT=1)_S 183 _t (final)_S 61 _t (answer)_S 61 _t (only)_S 2554 10914 _m (OUTPUT=2)_S 183 _t (initial)_S 61 _t (estimates)_S 61 _t (and)_S 61 _t (final)_S 61 _t (answer)_S 2554 10714 _m (OUTPUT=3)_S 183 _t (input)_S 61 _t (data)_S 61 _t (and)_S 61 _t (iteration)_S 61 _t (summaries)_S 2554 10514 _m (OUTPUT=4)_S 183 _t (detailed)_S 61 _t (summary)_S 61 _t (of)_S 61 _t (each)_S 61 _t (step)_S 2554 10314 _m (OUTPUT)_S /Symbol 550 _ff (\263)_S /Times-RomanR 550 _ff (5)_S 183 _t (very)_S 61 _t (detailed)_S 61 _t (summary)_S 61 _t (of)_S 61 _t (each)_S 61 _t (step)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 2567 _m _sp 2250 2567 2250 3001 2246 3001 3 _pl _f _s _s 100 _gs 1970 2997 _m _sp 2250 2997 2250 3001 1970 3001 3 _pl _f _s _s 100 _gs 1970 2567 _m _sp 1974 2567 1974 3001 1970 3001 3 _pl _f _s 429 271 1974 2567 _cw _s 3300 2550 674 801 _cw _s grestore 8292 11714 _m 61 _t 61 _t 61 _t 61 _t 61 _t (2)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 2563 _m _sp 610 2563 610 2567 300 2567 3 _pl _f _s _s 100 _gs 300 2233 _m _sp 304 2233 304 2567 300 2567 3 _pl _f _s 329 305 304 2233 _cw _s 3300 2550 674 801 _cw _s grestore 1480 9978 _m (QNUPDM)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 609 2563 _m _sp 1971 2563 1971 2567 609 2567 3 _pl _f _s _s 100 _gs 609 2233 _m _sp 613 2233 613 2567 609 2567 3 _pl _f _s 329 1357 613 2233 _cw _s 3300 2550 674 801 _cw _s grestore 2554 9978 _m (Quasi-Newton)_S 61 _t (update)_S 61 _t (method:)_S 2554 9778 _m (QNUPDM=0)_S 183 _t (unfactored)_S 61 _t (Jacobian)_S 61 _t (updated)_S 2554 9578 _m (QNUPDM=1)_S 183 _t (factored)_S 61 _t (Jacobian)_S 61 _t (updated)_S 2554 9378 _m (Mathematically)_S 61 _t (these)_S 61 _t (are)_S 61 _t (equivalent)_S 61 _t (although)_S 61 _t (numerically)_S 61 _t (they)_S 61 _t (may)_S 2554 9178 _m (give)_S 61 _t (slightly)_S 61 _t (different)_S 61 _t (results.)_S 122 _t (Use)_S 61 _t (QNUPDM=1)_S 61 _t (as)_S 61 _t (it)_S 61 _t (is)_S 61 _t (faster)_S 61 _t (unless)_S 2554 8978 _m (you)_S 61 _t (want)_S 61 _t (to)_S 61 _t (see)_S 61 _t (the)_S 61 _t (unfactored)_S 61 _t (updated)_S 61 _t (Jacobian.)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 2233 _m _sp 2250 2233 2250 2567 2246 2567 3 _pl _f _s _s 100 _gs 1970 2563 _m _sp 2250 2563 2250 2567 1970 2567 3 _pl _f _s _s 100 _gs 1970 2233 _m _sp 1974 2233 1974 2567 1970 2567 3 _pl _f _s 329 271 1974 2233 _cw _s 3300 2550 674 801 _cw _s grestore 8322 9978 _m 61 _t 61 _t 61 _t 61 _t (1)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 2229 _m _sp 610 2229 610 2233 300 2233 3 _pl _f _s _s 100 _gs 300 1899 _m _sp 304 1899 304 2233 300 2233 3 _pl _f _s 329 305 304 1899 _cw _s 3300 2550 674 801 _cw _s grestore 1531 8642 _m (STOPCR)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 609 2229 _m _sp 1971 2229 1971 2233 609 2233 3 _pl _f _s _s 100 _gs 609 1899 _m _sp 613 1899 613 2233 609 2233 3 _pl _f _s 329 1357 613 1899 _cw _s 3300 2550 674 801 _cw _s grestore 2554 8642 _m (Stopping)_S 61 _t (criterion,)_S 61 _t (the)_S 61 _t (following)_S 61 _t (must)_S 61 _t (be)_S 61 _t (met:)_S 2554 8442 _m (STOPCR=1)_S 244 _t (step)_S 61 _t (size)_S 61 _t (criterion)_S 61 _t (only)_S 2554 8242 _m (STOPCR=2)_S 244 _t (function)_S 61 _t (value)_S 61 _t (criterion)_S 61 _t (only)_S 2554 8042 _m (STOPCR=12)_S 183 _t (function)_S 61 _t (value)_S 61 _t /Times-ItalicR 550 _ff (or)_S /Times-RomanR 550 _ff 61 _t (step)_S 61 _t (size)_S 61 _t (criterion)_S 2554 7842 _m (STOPCR=3)_S 244 _t (function)_S 61 _t (value)_S 61 _t /Times-ItalicR 550 _ff (and)_S /Times-RomanR 550 _ff 61 _t (step)_S 61 _t (size)_S 61 _t (criteria)_S 2554 7642 _m (See)_S 61 _t (also)_S 61 _t (FTOL,)_S 61 _t (NSTTOL)_S 61 _t (and)_S 61 _t (STPTOL)_S 61 _t (for)_S 61 _t (details)_S 61 _t (of)_S 61 _t (each.)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 1899 _m _sp 2250 1899 2250 2233 2246 2233 3 _pl _f _s _s 100 _gs 1970 2229 _m _sp 2250 2229 2250 2233 1970 2233 3 _pl _f _s _s 100 _gs 1970 1899 _m _sp 1974 1899 1974 2233 1970 2233 3 _pl _f _s 329 271 1974 1899 _cw _s 3300 2550 674 801 _cw _s grestore 8276 8642 _m 61 _t 61 _t 61 _t 61 _t (12)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 1895 _m _sp 610 1895 610 1899 300 1899 3 _pl _f _s _s 100 _gs 300 1765 _m _sp 304 1765 304 1899 300 1899 3 _pl _f _s 129 305 304 1765 _cw _s 3300 2550 674 801 _cw _s grestore 1515 7306 _m (SUPPRS)_S 61 _t gsave 0 0 translate 4 4 scale _s _s 100 _gs 609 1895 _m _sp 1971 1895 1971 1899 609 1899 3 _pl _f _s _s 100 _gs 609 1765 _m _sp 613 1765 613 1899 609 1899 3 _pl _f _s 129 1357 613 1765 _cw _s 3300 2550 674 801 _cw _s grestore 2554 7306 _m (Suppresses)_S 61 _t (detailed)_S 61 _t (output)_S 61 _t (for)_S 61 _t (SUPPRS)_S 61 _t (iterations;)_S 61 _t (useful)_S 61 _t (if)_S 61 _t (failure)_S 61 _t (is)_S 2554 7106 _m (occurring)_S 61 _t (after)_S 61 _t (several)_S 61 _t (iterations)_S 61 _t (with)_S 61 _t (N)_S 61 _t (large.)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 1765 _m _sp 2250 1765 2250 1899 2246 1899 3 _pl _f _s _s 100 _gs 1970 1895 _m _sp 2250 1895 2250 1899 1970 1899 3 _pl _f _s _s 100 _gs 1970 1765 _m _sp 1974 1765 1974 1899 1970 1899 3 _pl _f _s 129 271 1974 1765 _cw _s 3300 2550 674 801 _cw _s grestore 8292 7306 _m 61 _t 61 _t 61 _t 61 _t 61 _t (0)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 1761 _m _sp 610 1761 610 1765 300 1765 3 _pl _f _s _s 100 _gs 300 1331 _m _sp 304 1331 304 1765 300 1765 3 _pl _f _s 429 305 304 1331 _cw _s 3300 2550 674 801 _cw _s grestore 1454 6770 _m (TRMCOD)_S 61 _t gsave 0 0 translate 4 4 scale _s _s 100 _gs 609 1761 _m _sp 1971 1761 1971 1765 609 1765 3 _pl _f _s _s 100 _gs 609 1331 _m _sp 613 1331 613 1765 609 1765 3 _pl _f _s 429 1357 613 1331 _cw _s 3300 2550 674 801 _cw _s grestore 2554 6770 _m (Termination)_S 61 _t (code)_S 61 _t (\(this)_S 61 _t (is)_S 61 _t (output)_S 61 _t (only\):)_S 2554 6570 _m (TRMCOD=0)_S 244 _t (problem)_S 61 _t (not)_S 61 _t (solved)_S 2554 6370 _m (TRMCOD=1)_S 244 _t (step)_S 61 _t (size)_S 61 _t (criterion)_S 61 _t (met)_S 2554 6170 _m (TRMCOD=12)_S 183 _t (step)_S 61 _t (size)_S 61 _t (and)_S 61 _t (function)_S 61 _t (value)_S 61 _t (criteria)_S 61 _t (met)_S 1098 _t 2554 5970 _m 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t (when)_S 61 _t (STOPCR=12)_S 2554 5770 _m (TRMCOD=2)_S 244 _t (function)_S 61 _t (value)_S 61 _t (stopping)_S 61 _t (criterion)_S 61 _t (met)_S 2554 5570 _m (TRMCOD=3)_S 244 _t (step)_S 61 _t (size)_S 61 _t (and)_S 61 _t (function)_S 61 _t (value)_S 61 _t (criteria)_S 61 _t (met)_S 61 _t (when)_S 671 _t 2554 5370 _m 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t (STOPCR=3)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 1331 _m _sp 2250 1331 2250 1765 2246 1765 3 _pl _f _s _s 100 _gs 1970 1761 _m _sp 2250 1761 2250 1765 1970 1765 3 _pl _f _s _s 100 _gs 1970 1331 _m _sp 1974 1331 1974 1765 1970 1765 3 _pl _f _s 429 271 1974 1331 _cw _s 3300 2550 674 801 _cw _s grestore 8307 6770 _m 61 _t 61 _t 61 _t 61 _t 61 _t (-)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 1327 _m _sp 610 1327 610 1331 300 1331 3 _pl _f _s _s 100 _gs 300 997 _m _sp 304 997 304 1331 300 1331 3 _pl _f _s 329 305 304 997 _cw _s 3300 2550 674 801 _cw _s grestore 1465 5034 _m (TRUPDM)_S 61 _t gsave 0 0 translate 4 4 scale _s _s 100 _gs 609 1327 _m _sp 1971 1327 1971 1331 609 1331 3 _pl _f _s _s 100 _gs 609 997 _m _sp 613 997 613 1331 609 1331 3 _pl _f _s 329 1357 613 997 _cw _s 3300 2550 674 801 _cw _s grestore 2554 5034 _m (Trust)_S 61 _t (region)_S 61 _t (update)_S 61 _t (method:)_S 2554 4834 _m (TRUPDM=0)_S 183 _t (Powell's)_S 61 _t (\(1970\))_S 61 _t (method)_S 61 _t (\(used)_S 61 _t (in)_S 61 _t (quasi-)_S 2554 4634 _m 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t (Newton)_S 61 _t (methods)_S 61 _t (only\))_S 2554 4434 _m (TRUPDM=1)_S 183 _t (Dennis)_S 61 _t (and)_S 61 _t (Schnabel's)_S 61 _t (\(1983\))_S 61 _t (method)_S 61 _t (\(can)_S 976 _t 2554 4234 _m 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t (be)_S 61 _t (used)_S 61 _t (in)_S 61 _t (quasi-Newton)_S 61 _t (methods,)_S 61 _t (must)_S 61 _t (be)_S 976 _t 2554 4034 _m 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t (used)_S 61 _t (otherwise\))_S 61 _t gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 997 _m _sp 2250 997 2250 1331 2246 1331 3 _pl _f _s _s 100 _gs 1970 1327 _m _sp 2250 1327 2250 1331 1970 1331 3 _pl _f _s _s 100 _gs 1970 997 _m _sp 1974 997 1974 1331 1970 1331 3 _pl _f _s 329 271 1974 997 _cw _s 3300 2550 674 801 _cw _s grestore 8292 5034 _m 61 _t 61 _t 61 _t 61 _t 61 _t (0)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 993 _m _sp 610 993 610 997 300 997 3 _pl _f _s _s 100 _gs 300 863 _m _sp 304 863 304 997 300 997 3 _pl _f _s 129 305 304 863 _cw _s 3300 2550 674 801 _cw _s grestore 1572 3698 _m (ALPHA)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 609 993 _m _sp 1971 993 1971 997 609 997 3 _pl _f _s _s 100 _gs 609 863 _m _sp 613 863 613 997 609 997 3 _pl _f _s 129 1357 613 863 _cw _s 3300 2550 674 801 _cw _s grestore 2554 3698 _m (Factor)_S 61 _t /Symbol 550 _ff (\316)_S /Times-RomanR 550 _ff 61 _t ([0,1\))_S 61 _t (in)_S 61 _t (function)_S 61 _t (value)_S 61 _t (step)_S 61 _t (acceptance)_S 61 _t (criterion.)_S 122 _t (See)_S 2554 3498 _m (description)_S 61 _t (of)_S 61 _t (MGLL)_S 61 _t (and)_S 61 _t (NARMIJ.)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 863 _m _sp 2250 863 2250 997 2246 997 3 _pl _f _s _s 100 _gs 1970 993 _m _sp 2250 993 2250 997 1970 997 3 _pl _f _s _s 100 _gs 1970 863 _m _sp 1974 863 1974 997 1970 997 3 _pl _f _s 129 271 1974 863 _cw _s 3300 2550 674 801 _cw _s grestore 8243 3698 _m (1.0E-4)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 859 _m _sp 610 859 610 863 300 863 3 _pl _f _s _s 100 _gs 300 579 _m _sp 304 579 304 863 300 863 3 _pl _f _s 279 305 304 579 _cw _s 3300 2550 674 801 _cw _s grestore 1505 3162 _m (CONFAC)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 609 859 _m _sp 1971 859 1971 863 609 863 3 _pl _f _s _s 100 _gs 609 579 _m _sp 613 579 613 863 609 863 3 _pl _f _s 279 1357 613 579 _cw _s 3300 2550 674 801 _cw _s grestore 2554 3162 _m (Factor)_S 61 _t /Symbol 550 _ff (\316)_S /Times-RomanR 550 _ff 61 _t (\(0,1])_S 61 _t (used)_S 61 _t (when)_S 61 _t (forcing)_S 61 _t (steps)_S 61 _t (to)_S 61 _t (stay)_S 61 _t (within)_S 61 _t (bounds;)_S 61 _t (the)_S 61 _t (trial)_S 2554 2962 _m (step)_S 61 _t (will)_S 61 _t (only)_S 61 _t (go)_S 61 _t (this)_S 61 _t (fraction)_S 61 _t (of)_S 61 _t (the)_S 61 _t (distance)_S 61 _t (to)_S 61 _t (the)_S 61 _t (first)_S 61 _t (bound)_S 2554 2762 _m (encountered)_S 61 _t (in)_S 61 _t (the)_S 61 _t (search)_S 61 _t (direction)_S 61 _t (in)_S 61 _t (line)_S 61 _t (search)_S 61 _t (methods)_S 61 _t (or,)_S 61 _t (in)_S 61 _t (trust)_S 2554 2562 _m (region)_S 61 _t (methods,)_S 61 _t (the)_S 61 _t (reduced)_S 61 _t (DELTA)_S 61 _t (will)_S 61 _t (be)_S 61 _t (this)_S 61 _t (fraction)_S 61 _t (of)_S 61 _t (the)_S 2554 2362 _m (distance)_S 61 _t (to)_S 61 _t (the)_S 61 _t (first)_S 61 _t (bound.)_S 183 _t gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 579 _m _sp 2250 579 2250 863 2246 863 3 _pl _f _s _s 100 _gs 1970 859 _m _sp 2250 859 2250 863 1970 863 3 _pl _f _s _s 100 _gs 1970 579 _m _sp 1974 579 1974 863 1970 863 3 _pl _f _s 279 271 1974 579 _cw _s 3300 2550 674 801 _cw _s grestore 8284 3162 _m 61 _t 61 _t 61 _t (.95)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 575 _m _sp 610 575 610 579 300 579 3 _pl _f _s _s 100 _gs 300 575 _m _sp 304 575 304 579 300 579 3 _pl _f _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 609 575 _m _sp 1971 575 1971 579 609 579 3 _pl _f _s _s 100 _gs 609 575 _m _sp 613 575 613 579 609 579 3 _pl _f _s grestore gsave 0 0 translate 4 4 scale _s _s 100 _gs 1970 575 _m _sp 2250 575 2250 579 1970 579 3 _pl _f _s _s 100 _gs 2246 575 _m _sp 2250 575 2250 579 2246 579 3 _pl _f _s _s 100 _gs 1970 575 _m _sp 1974 575 1974 579 1970 579 3 _pl _f _s grestore 4932 1250 _m (-)_S 61 _t (9)_S 61 _t (-)_S _ep _bp /Times-RomanR 550 _ff 0 13200 10200 _ornt /_r { sflg {/_t {0 rmoveto}bdef /ron false def} { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse }bdef gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 2997 _m _sp 610 2997 610 3001 300 3001 3 _pl _f _s _s 100 _gs 300 2817 _m _sp 304 2817 304 3001 300 3001 3 _pl _f _s 179 305 304 2817 _cw _s 3300 2550 674 801 _cw _s grestore 1577 11714 _m (DELTA)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 609 2997 _m _sp 1971 2997 1971 3001 609 3001 3 _pl _f _s _s 100 _gs 609 2817 _m _sp 613 2817 613 3001 609 3001 3 _pl _f _s 179 1357 613 2817 _cw _s 3300 2550 674 801 _cw _s grestore 2554 11714 _m (Trust)_S 61 _t (region)_S 61 _t (size)_S 61 _t (\(updated)_S 61 _t (internally\).)_S 122 _t (If)_S 61 _t (negative)_S 61 _t (on)_S 61 _t (input)_S 61 _t (NNES)_S 2554 11514 _m (calculates)_S 61 _t (the)_S 61 _t (first)_S 61 _t (trust)_S 61 _t (region)_S 61 _t (radius,)_S 61 _t (DELTA,)_S 61 _t (\(see)_S 61 _t (CAUCHY\))_S 61 _t (or)_S 61 _t (if)_S 2554 11314 _m (positive,)_S 61 _t (the)_S 61 _t (first)_S 61 _t (DELTA)_S 61 _t (is)_S 61 _t (the)_S 61 _t (input)_S 61 _t (value.)_S 61 _t gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 2817 _m _sp 2250 2817 2250 3001 2246 3001 3 _pl _f _s _s 100 _gs 1970 2997 _m _sp 2250 2997 2250 3001 1970 3001 3 _pl _f _s _s 100 _gs 1970 2817 _m _sp 1974 2817 1974 3001 1970 3001 3 _pl _f _s 179 271 1974 2817 _cw _s 3300 2550 674 801 _cw _s grestore 8284 11714 _m 61 _t 61 _t (-1.0)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 2813 _m _sp 610 2813 610 2817 300 2817 3 _pl _f _s _s 100 _gs 300 2633 _m _sp 304 2633 304 2817 300 2817 3 _pl _f _s 179 305 304 2633 _cw _s 3300 2550 674 801 _cw _s grestore 1521 10978 _m (DELFAC)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 609 2813 _m _sp 1971 2813 1971 2817 609 2817 3 _pl _f _s _s 100 _gs 609 2633 _m _sp 613 2633 613 2817 609 2817 3 _pl _f _s 179 1357 613 2633 _cw _s 3300 2550 674 801 _cw _s grestore 2554 10978 _m (Allows)_S 61 _t (changing)_S 61 _t (the)_S 61 _t (factor)_S 61 _t (by)_S 61 _t (which)_S 61 _t (trust)_S 61 _t (region)_S 61 _t (size,)_S 61 _t (DELTA,)_S 61 _t (is)_S 2554 10778 _m (modified)_S 61 _t (in)_S 61 _t (trust)_S 61 _t (region)_S 61 _t (updating)_S 61 _t (\(it)_S 61 _t (is)_S 61 _t (the)_S 61 _t (default)_S 61 _t (value)_S 61 _t (of)_S 61 _t (2.0)_S 61 _t (in)_S 61 _t (both)_S 2554 10578 _m (Powell's)_S 61 _t (\(1970\))_S 61 _t (and)_S 61 _t (Dennis)_S 61 _t (and)_S 61 _t (Schnabel's)_S 61 _t (\(1983\))_S 61 _t (methods\).)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 2633 _m _sp 2250 2633 2250 2817 2246 2817 3 _pl _f _s _s 100 _gs 1970 2813 _m _sp 2250 2813 2250 2817 1970 2817 3 _pl _f _s _s 100 _gs 1970 2633 _m _sp 1974 2633 1974 2817 1970 2817 3 _pl _f _s 179 271 1974 2633 _cw _s 3300 2550 674 801 _cw _s grestore 8284 10978 _m 61 _t 61 _t 61 _t (2.0)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 2629 _m _sp 610 2629 610 2633 300 2633 3 _pl _f _s _s 100 _gs 300 2337 _m _sp 304 2337 304 2633 300 2633 3 _pl _f _s 291 305 304 2337 _cw _s 3300 2550 674 801 _cw _s grestore 1510 10242 _m (EPSMCH)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 609 2629 _m _sp 1971 2629 1971 2633 609 2633 3 _pl _f _s _s 100 _gs 609 2337 _m _sp 613 2337 613 2633 609 2633 3 _pl _f _s 291 1357 613 2337 _cw _s 3300 2550 674 801 _cw _s grestore 2554 10242 _m (Machine)_S 61 _t (epsilon,)_S 61 _t /Symbol 550 _ff (e)_S /Times-RomanR 330 _ff 3973 10201 _m (m)_S 4059 10201 _m /Times-RomanR 550 _ff 4059 10242 _m (,)_S 61 _t (smallest)_S 61 _t (number,)_S 61 _t (x,)_S 61 _t (such)_S 61 _t (that:)_S gsave 0 0 translate 4 4 scale _s 3 _w 57 1282 663 2466 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale 1176 2514 48 _ieq FEFFFFFFFC1F 1392 2514 40 _ieq DFFFFFFF83 1176 2513 48 _ieq F8FFFFFFF007 1392 2513 40 _ieq 1FFFFFFE00 1176 2512 48 _ieq E0FFFFFFC001 1384 2512 56 _ieq FC1FFFFFF8003F 1176 2511 48 _ieq 80FFFFFFC7C1 1384 2511 56 _ieq F01FFFFFF8F83F 1168 2510 56 _ieq FE00FFFFFF87E0 1384 2510 56 _ieq C01FFFFFF0FC1F 1168 2509 64 _ieq FC00FFFFFF0FF07F 1384 2509 56 _ieq 801FFFFFE1FE0F 1168 2508 64 _ieq FDE0FFFFFF0FF03F 1384 2508 56 _ieq BC1FFFFFE1FE07 1176 2507 56 _ieq E0FFFFFE1FF83F 1336 2507 104 _ieq 9FFFFFFFFFFFFC1FFFFFC3FF07 1176 2506 56 _ieq E0FFFFFC1FF83F 1336 2506 104 _ieq 87FFFFFFFFFFFC1FFFFF83FF07 1176 2505 264 _ieq E0FFFFFC1FF83FFFFFFFFCFFFFFFFFFFFFFFFFFF80FFFFFFFFFFFC1FFFFF83FF07 1176 2504 264 _ieq E0FFFFFC1FF81FFFFFFFFCFFFFFFFFFC7C1FFFFF803FFFFFFFFFFC1FFFFF83FF03 1176 2503 264 _ieq E0FFFFF81FF81FFFFFFFFCFFFFFFFFC07C1FFFFFE007FFFFFFFFFC1FFFFF03FF03 1176 2502 264 _ieq E0FFFFF81FF81FFFFFFFFCFFFFFFFF80381FFFFFF801FFFFFFFFFC1FFFFF03FF03 1176 2501 264 _ieq E0FFFFF81FF81FFFFFFFFCFFFFFFFFB8381FFFFFFE003FFFFFFFFC1FFFFF03FF03 1176 2500 264 _ieq E0FFFFF81FF81FFFFFFFFCFFFFFFFFF8311FFFFFFFC00FFFFFFFFC1FFFFF03FF03 1176 2499 264 _ieq E0FFFFF81FF81FFFFFFFFCFFFFFFFFFC23FFFFFFFFF003FFFFFFFC1FFFFF03FF03 1176 2498 264 _ieq E0FFFFF81FF81FFFFFFFFCFFFFFFFFFC07FFFFFFFFFC03FFFFFFFC1FFFFF03FF03 1176 2497 264 _ieq E0FFFFF81FF81FFFFFFC0000FFFFFFFE0FFFFFFFFFFF03FFFFFFFC1FFFFF03FF03 1176 2496 264 _ieq E0FFFFF81FF81FFFFFFC0000FFFFFFFE1FFFFFFFFFF803FFFFFFFC1FFFFF03FF03 1176 2495 264 _ieq E0FFFFF81FF81FFFFFFFFCFFFFFFFFFE1FFFFFFFFFE00FFFFFFFFC1FFFFF03FF03 1176 2494 264 _ieq E0FFFFF81FF81FFFFFFFFCFFFFFFFFFE1FFFFFFFFF003FFFFFFFFC1FFFFF03FF03 1176 2493 264 _ieq E0FFFFFC1FF81FFFFFFFFCFFFFFFFFFE1FFFFFFFF800FFFFFFFFFC1FFFFF83FF03 1176 2492 264 _ieq E0FFFFFC1FF81FFFFFFFFCFFFFFFFFFE0FFFFFFFE003FFFFFFFFFC1FFFFF83FF03 1176 2491 264 _ieq E0FFFFFE0FF81FFFFFFFFCFFFFFFFFFC0FFFFFFF801FFFFFFFFFFC1FFFFFC1FF03 1176 2490 264 _ieq E0FFFFFE0FF83FFFFFFFFCFFFFFFFFF80FFFFFFF807FFFFFFFFFFC1FFFFFC1FF07 1176 2489 264 _ieq E0FFFFFE0FF03FFFFFFFFCFFFFFFFFF807FFFFFF81FFFFFFFFFFFC1FFFFFC1FE07 1176 2488 264 _ieq E0FFF0FE07F03FFFFFFFFCFFFFFFFFF3073FFFFF87FFFFFFFFFFFC1FFE1FC0FE07 1176 2487 264 _ieq E0FFF0FE07F07FFFFFFFFFFFFFFFFFF7073FFFFF9FFFFFFFFFFFFC1FFE1FC0FE0F 1176 2486 264 _ieq E0FFE07F03E0FFFFFFFFFFFFFFFFF067863FFFFFFFFFFFFFFFFFFC1FFC0FE07C1F 1176 2485 264 _ieq E07FE07F83C0FFFFFFFFFFFFFFFFF00F807FFFFFFFFFFFFFFFFFFC0FFC0FF0781F 1168 2484 272 _ieq FE000FE07FE001FFFFFFFFFFFFFFFFF01F80FFFFFFFFFFFFFFFFFFC001FC0FFC003F 1168 2483 272 _ieq FE000FE07FE003FFFFFFFFFFFFFFFFF01F81FFFFFFFFFFFFFFFFFFC001FC0FFC007F 1192 2482 120 _ieq F0FFF007FFFFFFFFFFFFFFFFF03FC3 1400 2482 32 _ieq FE1FFE00 1192 2481 120 _ieq F8FFF80FFFFFFFFFFFFFFFFFF87FE7 1408 2481 24 _ieq 1FFF01 _s grestore gsave 0 0 translate 4 4 scale _s 1 _w _s 100 _gs 2246 2337 _m _sp 2250 2337 2250 2633 2246 2633 3 _pl _f _s _s 100 _gs 1970 2629 _m _sp 2250 2629 2250 2633 1970 2633 3 _pl _f _s _s 100 _gs 1970 2337 _m _sp 1974 2337 1974 2633 1970 2633 3 _pl _f _s 291 271 1974 2337 _cw _s 3300 2550 674 801 _cw _s grestore 8225 10242 _m 61 _t (set)_S 61 _t (in)_S 61 _t 8251 10042 _m (NNES)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 2333 _m _sp 610 2333 610 2337 300 2337 3 _pl _f _s _s 100 _gs 300 2053 _m _sp 304 2053 304 2337 300 2337 3 _pl _f _s 279 305 304 2053 _cw _s 3300 2550 674 801 _cw _s grestore 1521 9058 _m (ETAFAC)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 609 2333 _m _sp 1971 2333 1971 2337 609 2337 3 _pl _f _s _s 100 _gs 609 2053 _m _sp 613 2053 613 2337 609 2337 3 _pl _f _s 279 1357 613 2053 _cw _s 3300 2550 674 801 _cw _s grestore 2554 9058 _m (Allows)_S 61 _t (switching)_S 61 _t (between)_S 61 _t (dogleg)_S 61 _t (and)_S 61 _t (double)_S 61 _t (dogleg)_S 61 _t (method)_S 61 _t (\(see)_S 2554 8858 _m (Dennis)_S 61 _t (and)_S 61 _t (Mei)_S 61 _t (\(1979\))_S 61 _t (or)_S 61 _t (Dennis)_S 61 _t (and)_S 61 _t (Schnabel)_S 61 _t (\(1983\))_S 61 _t (or)_S 61 _t (description)_S 2554 8658 _m (in)_S 61 _t (Section)_S 61 _t (3\):)_S 2554 8458 _m (ETAFAC)_S 61 _t (=)_S 61 _t (1.0)_S 366 _t (single)_S 61 _t (dogleg)_S 61 _t (method)_S 2554 8258 _m (ETAFAC)_S 61 _t /Symbol 550 _ff (\316)_S /Times-RomanR 550 _ff 61 _t (\(0,1\))_S 244 _t (double)_S 61 _t (dogleg)_S 61 _t (method)_S 61 _t gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 2053 _m _sp 2250 2053 2250 2337 2246 2337 3 _pl _f _s _s 100 _gs 1970 2333 _m _sp 2250 2333 2250 2337 1970 2337 3 _pl _f _s _s 100 _gs 1970 2053 _m _sp 1974 2053 1974 2337 1970 2337 3 _pl _f _s 279 271 1974 2053 _cw _s 3300 2550 674 801 _cw _s grestore 8284 9058 _m 61 _t 61 _t 61 _t (0.2)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 2049 _m _sp 610 2049 610 2053 300 2053 3 _pl _f _s _s 100 _gs 300 1549 _m _sp 304 1549 304 2053 300 2053 3 _pl _f _s 499 305 304 1549 _cw _s 3300 2550 674 801 _cw _s grestore 1546 7922 _m (FDTOLJ)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 609 2049 _m _sp 1971 2049 1971 2053 609 2053 3 _pl _f _s _s 100 _gs 609 1549 _m _sp 613 1549 613 2053 609 2053 3 _pl _f _s 499 1357 613 1549 _cw _s 3300 2550 674 801 _cw _s grestore 2554 7922 _m (Tolerance)_S 61 _t (in)_S 61 _t (comparing)_S 61 _t (the)_S 61 _t (analytical)_S 61 _t (Jacobian,)_S 61 _t (JAC,)_S 61 _t (to)_S 61 _t (the)_S 61 _t (forward)_S 2554 7722 _m (finite-difference)_S 61 _t (check,)_S 61 _t (JACFD.)_S 122 _t (The)_S 61 _t (program)_S 61 _t (stops)_S 61 _t (if)_S 2554 7522 _m 61 _t 2554 6242 _m (NJACCH)_S 61 _t (controls)_S 61 _t (how)_S 61 _t (many)_S 61 _t (times)_S 61 _t (the)_S 61 _t (Jacobian)_S 61 _t (is)_S 61 _t (checked.)_S gsave 0 0 translate 4 4 scale _s 3 _w 145 1282 663 1698 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale 872 1832 8 _ieq F9 976 1832 8 _ieq C7 1176 1832 96 _ieq 1FFFFFFFFFFFFFFFFFFFFC7F 1392 1832 16 _ieq FE3F 1496 1832 8 _ieq 3F 872 1831 8 _ieq F9 976 1831 8 _ieq C7 1176 1831 96 _ieq 1FFFFFFFFFFFFFFFFFFFFC7F 1392 1831 16 _ieq FE3F 1496 1831 8 _ieq 9F 872 1830 8 _ieq F3 976 1830 8 _ieq C7 1176 1830 96 _ieq 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FC7FFFFFFFFFFFFFFE3FFFFFFF8F _s grestore gsave 0 0 translate 4 4 scale _s 1 _w _s 100 _gs 2246 1365 _m _sp 2250 1365 2250 2039 2246 2039 3 _pl _f _s _s 100 _gs 1970 2035 _m _sp 2250 2035 2250 2039 1970 2039 3 _pl _f _s _s 100 _gs 1970 1365 _m _sp 1974 1365 1974 2039 1970 2039 3 _pl _f _s 669 271 1974 1365 _cw _s 3300 2550 674 801 _cw _s grestore 8284 7866 _m 61 _t 61 _t 61 _t (0.1)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 1361 _m _sp 610 1361 610 1365 300 1365 3 _pl _f _s _s 100 _gs 300 699 _m _sp 304 699 304 1365 300 1365 3 _pl _f _s 661 305 304 699 _cw _s 3300 2550 674 801 _cw _s grestore 1516 5170 _m 61 _t (RATIOF)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 609 1361 _m _sp 1971 1361 1971 1365 609 1365 3 _pl _f _s _s 100 _gs 609 699 _m _sp 613 699 613 1365 609 1365 3 _pl _f _s 661 1357 613 699 _cw _s 3300 2550 674 801 _cw _s grestore 2554 5170 _m (Comparison)_S 61 _t (factor)_S 61 _t /Symbol 550 _ff (\316)_S /Times-RomanR 550 _ff 61 _t (\(0,1])_S 61 _t (in)_S 61 _t 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56 _ieq F870E007E2431F 1264 2793 40 _ieq 87E1C787E3 1088 2792 56 _ieq F8F1E00FE0433F 1264 2792 40 _ieq 87E1C78FC3 1088 2791 56 _ieq F8E1E1FFE0C27F 1264 2791 40 _ieq 87E3878F87 1088 2790 48 _ieq F1E161FFE0E0 1264 2790 40 _ieq 87C78D0F85 1088 2789 48 _ieq F1E121FBE1E0 1264 2789 40 _ieq 87CF8C0F84 1088 2788 48 _ieq F1E061E3E1E1 1264 2788 40 _ieq 870F090E00 1088 2787 48 _ieq E3E0F007E3E1 1264 2787 40 _ieq C01F038081 1088 2786 48 _ieq E3E0F00FE3E3 1264 2786 40 _ieq C03F078183 1096 2785 40 _ieq F1F83FE7F7 1264 2785 40 _ieq E07F8FC38F _s grestore gsave 0 0 translate 4 4 scale _s 1 _w _s 100 _gs 2246 2655 _m _sp 2250 2655 2250 3001 2246 3001 3 _pl _f _s _s 100 _gs 1970 2997 _m _sp 2250 2997 2250 3001 1970 3001 3 _pl _f _s _s 100 _gs 1970 2655 _m _sp 1974 2655 1974 3001 1970 3001 3 _pl _f _s 341 271 1974 2655 _cw _s 3300 2550 674 801 _cw _s grestore 8284 11714 _m 61 _t 61 _t 61 _t (0.5)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 2651 _m _sp 610 2651 610 2655 300 2655 3 _pl _f _s _s 100 _gs 300 2101 _m _sp 304 2101 304 2655 300 2655 3 _pl _f _s 549 305 304 2101 _cw _s 3300 2550 674 801 _cw _s grestore 1541 10330 _m (STPTOL)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 609 2651 _m _sp 1971 2651 1971 2655 609 2655 3 _pl _f _s _s 100 _gs 609 2101 _m _sp 613 2101 613 2655 609 2655 3 _pl _f _s 549 1357 613 2101 _cw _s 3300 2550 674 801 _cw _s grestore 2554 10330 _m (Stopping)_S 61 _t (tolerance)_S 61 _t (for)_S 61 _t (the)_S 61 _t (step)_S 61 _t (size.)_S 61 _t 2554 9050 _m (This)_S 61 _t (governs)_S 61 _t (the)_S 61 _t (step)_S 61 _t (size)_S 61 _t (after)_S 61 _t (the)_S 61 _t (line)_S 61 _t (search)_S 61 _t (or)_S 61 _t (trust)_S 61 _t (region)_S gsave 0 0 translate 4 4 scale _s 3 _w 163 1282 663 2382 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale 952 2534 8 _ieq CF 1472 2534 8 _ieq F9 952 2533 8 _ieq CF 1472 2533 8 _ieq FC 952 2532 8 _ieq 9F 1120 2532 8 _ieq 8F 1312 2532 8 _ieq C7 1472 2532 16 _ieq FC7F 952 2531 8 _ieq 1F 1120 2531 8 _ieq 8F 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_pl _f _s _s 100 _gs 1970 2651 _m _sp 2250 2651 2250 2655 1970 2655 3 _pl _f _s _s 100 _gs 1970 2101 _m _sp 1974 2101 1974 2655 1970 2655 3 _pl _f _s 549 271 1974 2101 _cw _s 3300 2550 674 801 _cw _s grestore 8245 10330 _m 61 _t 61 _t 61 _t /Symbol 550 _ff (e)_S /Times-RomanR 330 _ff 8509 10289 _m (m)_S 8594 10330 _m 8594 10405 _m (2/3)_S /Times-RomanR 550 _ff gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 2097 _m _sp 610 2097 610 2101 300 2101 3 _pl _f _s _s 100 _gs 300 1967 _m _sp 304 1967 304 2101 300 2101 3 _pl _f _s 129 305 304 1967 _cw _s 3300 2550 674 801 _cw _s grestore 1495 8114 _m (BOUNDL)_S 1485 7914 _m (BOUNDU)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 609 2097 _m _sp 1971 2097 1971 2101 609 2101 3 _pl _f _s _s 100 _gs 609 1967 _m _sp 613 1967 613 2101 609 2101 3 _pl _f _s 129 1357 613 1967 _cw _s 3300 2550 674 801 _cw _s grestore 2554 8114 _m (Vectors)_S 61 _t (containing)_S 61 _t (lower)_S 61 _t (and)_S 61 _t (upper)_S 61 _t (bounds)_S 61 _t (for)_S 61 _t (the)_S 61 _t (components.)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 1967 _m _sp 2250 1967 2250 2101 2246 2101 3 _pl _f _s _s 100 _gs 1970 2097 _m _sp 2250 2097 2250 2101 1970 2101 3 _pl _f _s _s 100 _gs 1970 1967 _m _sp 1974 1967 1974 2101 1970 2101 3 _pl _f _s 129 271 1974 1967 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale 100 _gs 3 _w 100 _gs 2042 2029 _m _sp 2042 2029 2042 2036 2050 2036 2050 2037 2042 2037 2042 2045 2041 2045 2041 2037 2033 2037 2033 2036 2041 2036 2041 2029 12 _pl _cp 100 _gs 2033 2047 _m _sp 2033 2047 2050 2047 2050 2048 2033 2048 4 _pl _cp _f _s grestore 8110 8114 _m 8222 8114 _m (10)_S /Times-RomanR 330 _ff 8406 8189 _m (MAXEXP)_S /Times-RomanR 550 _ff gsave 0 0 translate 4 4 scale _s 1 _w _s 100 _gs 300 1963 _m _sp 610 1963 610 1967 300 1967 3 _pl _f _s _s 100 _gs 300 1783 _m _sp 304 1783 304 1967 300 1967 3 _pl _f _s 179 305 304 1783 _cw _s 3300 2550 674 801 _cw _s grestore 1536 7578 _m (SCALEF)_S 1521 7378 _m (SCALEX)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 609 1963 _m _sp 1971 1963 1971 1967 609 1967 3 _pl _f _s _s 100 _gs 609 1783 _m _sp 613 1783 613 1967 609 1967 3 _pl _f _s 179 1357 613 1783 _cw _s 3300 2550 674 801 _cw _s grestore 2554 7578 _m (Vectors)_S 61 _t (containing)_S 61 _t (scaling)_S 61 _t (factors)_S 61 _t (for)_S 61 _t (the)_S 61 _t (functions)_S 61 _t (and)_S 61 _t (the)_S 2554 7378 _m (components,)_S 61 _t (respectively.)_S 122 _t (These)_S 61 _t (can)_S 61 _t (be)_S 61 _t (set)_S 61 _t (permanently)_S 61 _t (by)_S 61 _t (the)_S 61 _t (user)_S 2554 7178 _m (or)_S 61 _t (updated)_S 61 _t (internally)_S 61 _t (\(see)_S 61 _t (ITSCLF)_S 61 _t (and)_S 61 _t (ITSCLX\).)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 2246 1783 _m _sp 2250 1783 2250 1967 2246 1967 3 _pl _f _s _s 100 _gs 1970 1963 _m _sp 2250 1963 2250 1967 1970 1967 3 _pl _f _s _s 100 _gs 1970 1783 _m _sp 1974 1783 1974 1967 1970 1967 3 _pl _f _s 179 271 1974 1783 _cw _s 3300 2550 674 801 _cw _s grestore 8375 7578 _m (1.0)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 300 1645 _m _sp 610 1645 610 1649 300 1649 3 _pl _f _s _s 100 _gs 300 1779 _m _sp 610 1779 610 1783 300 1783 3 _pl _f _s _s 100 _gs 300 1645 _m _sp 304 1645 304 1783 300 1783 3 _pl _f _s 129 305 304 1649 _cw _s 3300 2550 674 801 _cw _s grestore 1617 6842 _m (HELP)_S 61 _t gsave 0 0 translate 4 4 scale _s _s 100 _gs 609 1645 _m _sp 1971 1645 1971 1649 609 1649 3 _pl _f _s _s 100 _gs 609 1779 _m _sp 1971 1779 1971 1783 609 1783 3 _pl _f _s _s 100 _gs 609 1645 _m _sp 613 1645 613 1783 609 1783 3 _pl _f _s 129 1357 613 1649 _cw _s 3300 2550 674 801 _cw _s grestore 2554 6842 _m (Designates)_S 61 _t (variables)_S 61 _t (to)_S 61 _t (be)_S 61 _t (described)_S 61 _t (using)_S 61 _t (on-line)_S 61 _t (help)_S 61 _t (facility)_S 61 _t (\(see)_S 2554 6642 _m (below\).)_S gsave 0 0 translate 4 4 scale _s _s 100 _gs 1970 1645 _m _sp 2250 1645 2250 1649 1970 1649 3 _pl _f _s _s 100 _gs 2246 1645 _m _sp 2250 1645 2250 1783 2246 1783 3 _pl _f _s _s 100 _gs 1970 1779 _m _sp 2250 1779 2250 1783 1970 1783 3 _pl _f _s _s 100 _gs 1970 1645 _m _sp 1974 1645 1974 1783 1970 1783 3 _pl _f _s 129 271 1974 1649 _cw _s 3300 2550 674 801 _cw _s grestore 8174 6842 _m 61 _t 61 _t (NONE)_S 2937 6226 _m (Table)_S 61 _t (2)_S 122 _t (Description)_S 61 _t (and)_S 61 _t (Defaults)_S 61 _t (for)_S 61 _t (User-set)_S 61 _t (Variables)_S 61 _t 1200 5426 _m /Times-BoldR 550 _ff (2.1)_S 61 _t (Using)_S 61 _t (NNES's)_S 61 _t (Help)_S 61 _t (Facility)_S /Times-RomanR 550 _ff 1800 5026 _m (A)_S 60 _t (brief)_S 60 _t (description)_S 59 _t (of)_S 60 _t (the)_S 60 _t (variables)_S 59 _t (in)_S 60 _t (Table)_S 59 _t (2)_S 60 _t (may)_S 60 _t (be)_S 59 _t (obtained)_S 60 _t (from)_S 60 _t (the)_S 60 _t (help)_S 59 _t (facility)_S 60 _t (in)_S 59 _t (NNES.)_S 1200 4826 _m (The)_S 63 _t (default)_S 63 _t (for)_S 63 _t (the)_S 62 _t (CHARACTER)_S 63 _t (variable)_S 63 _t (HELP)_S 62 _t (is)_S 63 _t (NONE.)_S 125 _t (If)_S 63 _t (a)_S 63 _t (description)_S 62 _t (of)_S 63 _t (any)_S 63 _t (particular)_S 62 _t (variable)_S 1200 4626 _m (is)_S 55 _t (desired,)_S 54 _t (set)_S 54 _t (HELP='variable)_S 54 _t (name',)_S 54 _t (e.g.,)_S 54 _t (for)_S 54 _t (a)_S 54 _t (description)_S 55 _t (of)_S 54 _t (CAUCHY)_S 54 _t (set)_S 54 _t (HELP='CAUCHY')_S 54 _t (before)_S 1200 4426 _m (the)_S 69 _t (call)_S 69 _t (to)_S 69 _t (NNES.)_S 137 _t (If)_S 69 _t (the)_S 69 _t (help)_S 69 _t (facility)_S 69 _t (is)_S 69 _t (used)_S 69 _t (the)_S 69 _t (program)_S 69 _t (will)_S 69 _t (stop)_S 69 _t (after)_S 69 _t (printing)_S 69 _t (a)_S 69 _t (description)_S 69 _t (of)_S 69 _t (the)_S 1200 4226 _m (variable\(s\).)_S 1800 4026 _m (If)_S 61 _t (any)_S 61 _t (family)_S 61 _t (of)_S 61 _t (variables)_S 61 _t (is)_S 61 _t (desired,)_S 61 _t (set)_S 61 _t (HELP)_S 61 _t (to:)_S 2400 3626 _m (ALLLOG)_S 3600 3626 _m (all)_S 61 _t (logical)_S 61 _t (variables)_S 2400 3426 _m (ALLINT)_S 3600 3426 _m (all)_S 61 _t (integer)_S 61 _t (variables)_S 2400 3226 _m (ALLREA)_S 3600 3226 _m (all)_S 61 _t (real)_S 61 _t (variables)_S 61 _t 2400 3026 _m (ALLMAT)_S 3600 3026 _m (all)_S 61 _t (arrays)_S 61 _t (\(including)_S 61 _t (vectors\))_S 1200 2626 _m (or,)_S 77 _t (if)_S 76 _t (the)_S 77 _t (complete)_S 77 _t (list)_S 77 _t (is)_S 77 _t (desired,)_S 77 _t (set)_S 77 _t (HELP)_S 77 _t (to)_S 77 _t (ALL.)_S 154 _t (The)_S 76 _t (variable)_S 77 _t (name)_S 77 _t (must)_S 77 _t (be)_S 77 _t (left)_S 77 _t (justified,)_S 77 _t (e.g.,)_S 1200 2426 _m (HELP='ALL')_S 58 _t (is)_S 58 _t (correct)_S 59 _t (while)_S 58 _t (HELP=')_S 174 _t (ALL')_S 59 _t (fails.)_S 116 _t (The)_S 58 _t (help)_S 58 _t (facility)_S 58 _t (is)_S 58 _t (designed)_S 59 _t (to)_S 58 _t (provide)_S 58 _t (reminders)_S 1200 2226 _m (to)_S 61 _t (a)_S 61 _t (user)_S 61 _t (familiar)_S 61 _t (with)_S 61 _t (NNES;)_S 61 _t (the)_S 61 _t (descriptions)_S 61 _t (are)_S 61 _t (less)_S 61 _t (detailed)_S 61 _t (than)_S 61 _t (those)_S 61 _t (provided)_S 61 _t (in)_S 61 _t (the)_S 61 _t (manual.)_S 4886 1250 _m (-)_S 61 _t (12)_S 61 _t (-)_S _ep _bp /Times-RomanR 550 _ff 0 13200 10200 _ornt /_r { sflg {/_t {0 rmoveto}bdef /ron false def} { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse }bdef 1200 11850 _m /Times-BoldR 550 _ff (2.2)_S 61 _t (Making)_S 61 _t (Changes)_S 61 _t (to)_S 61 _t (the)_S 61 _t (Default)_S 61 _t (Settings)_S /Times-RomanR 550 _ff 1620 11450 _m (If)_S 63 _t (the)_S 63 _t (default)_S 63 _t (settings)_S 63 _t (fail)_S 63 _t (to)_S 63 _t (provide)_S 63 _t (the)_S 63 _t (correct)_S 64 _t (solution,)_S 63 _t (then)_S 63 _t (the)_S 63 _t (following)_S 63 _t (general)_S 63 _t (rules)_S 63 _t (may)_S 64 _t (be)_S 1200 11250 _m (useful)_S 73 _t (to)_S 73 _t (decide)_S 74 _t (which)_S 73 _t (of)_S 73 _t (NNES's)_S 73 _t (many)_S 73 _t (options)_S 74 _t (should)_S 73 _t (be)_S 73 _t (changed.)_S 147 _t (This)_S 73 _t (is)_S 73 _t (followed)_S 73 _t (by)_S 73 _t (a)_S 74 _t (series)_S 73 _t (of)_S 1200 11050 _m (suggestions)_S 61 _t (for)_S 61 _t (specific)_S 61 _t (situations.)_S 1200 10650 _m (1.)_S 1620 10650 _m (Generally)_S 46 _t (the)_S 46 _t (most)_S 47 _t (effective)_S 46 _t (way)_S 46 _t (to)_S 46 _t (find)_S 47 _t (a)_S 46 _t (difficult)_S 46 _t (solution)_S 46 _t (is)_S 47 _t (to)_S 46 _t /Times-BoldR 550 _ff (try)_S 46 _t (different)_S 46 _t (starting)_S 46 _t (points)_S /Times-RomanR 550 _ff (.)_S 93 _t (This)_S 1620 10450 _m (will)_S 63 _t (also)_S 64 _t (confirm)_S 63 _t (the)_S 63 _t (uniqueness)_S 63 _t (of)_S 63 _t (a)_S 64 _t (solution)_S 63 _t (or,)_S 63 _t (possibly,)_S 63 _t (reveal)_S 63 _t (multiple)_S 64 _t (solutions.)_S 126 _t (This)_S 63 _t (shows)_S 1620 10250 _m (the)_S 76 _t (ultimate)_S 75 _t (weakness)_S 75 _t (of)_S 75 _t (Newton-based)_S 75 _t (nonlinear)_S 76 _t (equations)_S 75 _t (solvers;)_S 75 _t (you)_S 75 _t (must)_S 75 _t (be)_S 76 _t ("close")_S 75 _t (to)_S 75 _t (the)_S 1620 10050 _m (solution)_S 61 _t (before)_S 61 _t (you)_S 61 _t (can)_S 61 _t (find)_S 61 _t (it.)_S 1200 9650 _m (2.)_S 1620 9650 _m /Times-BoldR 550 _ff (Changing)_S 52 _t (to)_S 52 _t (an)_S 52 _t (undamped)_S 52 _t (Newton's)_S 53 _t (method)_S /Times-RomanR 550 _ff 52 _t (is)_S 52 _t (unlikely)_S 52 _t (to)_S 52 _t (find)_S 52 _t (solutions)_S 52 _t (that)_S 52 _t (the)_S 52 _t (default)_S 52 _t (method)_S 1620 9450 _m (won't)_S 76 _t (find,)_S 77 _t (although)_S 76 _t (there)_S 77 _t (are)_S 76 _t (some)_S 77 _t (problems)_S 76 _t (where)_S 77 _t (a)_S 76 _t (Newton)_S 77 _t (step)_S 76 _t (just)_S 77 _t (happens)_S 76 _t (to)_S 77 _t (land)_S 76 _t (at)_S 77 _t (the)_S 1620 9250 _m (correct)_S 53 _t (spot.)_S 107 _t (One)_S 54 _t (strategy,)_S 53 _t (however,)_S 54 _t (is)_S 54 _t (to)_S 53 _t (let)_S 54 _t (Newton's)_S 53 _t (method)_S 54 _t (run)_S 53 _t (without)_S 54 _t (bounds)_S 54 _t (until)_S 53 _t (a)_S 54 _t (solution)_S 1620 9050 _m (is)_S 63 _t (found)_S 64 _t (then)_S 64 _t (adjust)_S 64 _t (the)_S 63 _t (infeasible)_S 64 _t (solution)_S 63 _t (components)_S 64 _t (and)_S 64 _t (run)_S 64 _t (using)_S 63 _t (default)_S 64 _t (settings)_S 64 _t (and)_S 64 _t (bounds)_S 1620 8850 _m (or)_S 59 _t (switch)_S 59 _t (to)_S 60 _t (Absolute)_S 59 _t (Newton's)_S 59 _t (method)_S 60 _t (and)_S 59 _t (bounds.)_S 118 _t (The)_S 60 _t /Times-BoldR 550 _ff (trust)_S 59 _t (region)_S 59 _t (method)_S /Times-RomanR 550 _ff 60 _t (is)_S 59 _t (about)_S 60 _t (as)_S 59 _t (robust)_S 1620 8650 _m (as)_S 47 _t (the)_S 47 _t (line)_S 47 _t (search)_S 48 _t (method.)_S 94 _t (Because)_S 47 _t (of)_S 48 _t (different)_S 47 _t (search)_S 47 _t (directions)_S 47 _t (it)_S 48 _t (may)_S 47 _t (find)_S 47 _t (different)_S 47 _t (solutions)_S 48 _t (than)_S 1620 8450 _m (the)_S 61 _t (default)_S 61 _t (but)_S 61 _t (not)_S 61 _t (usually.)_S 1200 8050 _m (3.)_S 1620 8050 _m /Times-BoldR 550 _ff (Bounds)_S /Times-RomanR 550 _ff 58 _t (usually)_S 57 _t (greatly)_S 58 _t (affect)_S 58 _t (performance.)_S 116 _t (There)_S 58 _t (is)_S 58 _t (a)_S 57 _t (chance,)_S 58 _t (however,)_S 58 _t (that)_S 58 _t (the)_S 58 _t (program)_S 58 _t (will)_S 58 _t (get)_S 1620 7850 _m (stuck)_S 66 _t (at)_S 67 _t (a)_S 66 _t (boundary)_S 66 _t (so)_S 67 _t (it)_S 66 _t (is)_S 66 _t (best)_S 66 _t (to)_S 67 _t (leave)_S 66 _t (bounds)_S 67 _t (off)_S 66 _t (initially)_S 66 _t (then)_S 66 _t (apply)_S 67 _t (if)_S 66 _t (necessary.)_S 133 _t (If)_S 66 _t (you)_S 66 _t (use)_S 1620 7650 _m (bounds,)_S 54 _t (try)_S 53 _t (not)_S 54 _t (to)_S 53 _t (use)_S 54 _t (an)_S 54 _t (initial)_S 53 _t (estimate)_S 54 _t (at)_S 53 _t (the)_S 54 _t (bound;)_S 53 _t (leave)_S 54 _t (the)_S 53 _t (program)_S 54 _t (room)_S 54 _t (to)_S 53 _t (move)_S 54 _t (either)_S 53 _t (way.)_S 1200 7450 _m 61 _t 1200 7250 _m (4.)_S 1620 7250 _m /Times-BoldR 550 _ff (Scaling)_S /Times-RomanR 550 _ff 57 _t (probably)_S 58 _t (won't)_S 57 _t (help)_S 58 _t (if)_S 57 _t (no)_S 57 _t (solution)_S 58 _t (is)_S 57 _t (being)_S 57 _t (found)_S 58 _t (unless)_S 57 _t (the)_S 57 _t (problem)_S 58 _t (is)_S 57 _t (very)_S 58 _t (badly)_S 57 _t (scaled.)_S 1620 7050 _m (It)_S 60 _t (does)_S 61 _t (affect)_S 60 _t (performance)_S 60 _t (however.)_S 121 _t (User-selected)_S 60 _t (scaling)_S 60 _t (factors)_S 61 _t (are)_S 60 _t (generally)_S 60 _t (the)_S 61 _t (best.)_S 120 _t (Look)_S 61 _t (at)_S 1620 6850 _m (the)_S 63 _t (function)_S 63 _t (values)_S 63 _t (from)_S 63 _t (a)_S 63 _t (detailed)_S 63 _t (output)_S 63 _t (and)_S 63 _t (judge)_S 63 _t (which)_S 62 _t (functions)_S 63 _t (are)_S 63 _t (contributing)_S 63 _t (most)_S 63 _t (to)_S 63 _t (the)_S 1620 6650 _m (objective)_S 44 _t (function)_S 44 _t (then)_S 44 _t (set)_S 44 _t (scaling)_S 44 _t (factors,)_S 44 _t (SCALEF)_S /Times-RomanR 330 _ff 5433 6609 _m (i)_S 5464 6609 _m /Times-RomanR 550 _ff 5464 6650 _m (,)_S 44 _t (so)_S 43 _t (that)_S 44 _t (when)_S 44 _t (multiplied)_S 44 _t (by)_S 44 _t (the)_S 44 _t (function)_S 43 _t (a)_S 44 _t (result)_S 1620 6450 _m (of)_S 61 _t /Times-ItalicR 550 _ff (O)_S /Times-RomanR 550 _ff (\(1\))_S 61 _t (is)_S 61 _t (found.)_S 1200 6050 _m (5.)_S 1620 6050 _m (Switching)_S 70 _t (to)_S 71 _t (a)_S 70 _t /Times-BoldR 550 _ff (quasi-Newton)_S 70 _t (method)_S /Times-RomanR 550 _ff 71 _t (will)_S 70 _t (likely)_S 70 _t (slow)_S 71 _t (down)_S 70 _t (the)_S 70 _t (solution)_S 71 _t (in)_S 70 _t (terms)_S 70 _t (of)_S 71 _t (number)_S 70 _t (of)_S 1620 5850 _m (iterations)_S 75 _t (and)_S 76 _t (time,)_S 75 _t (unless)_S 76 _t (the)_S 75 _t (functions)_S 76 _t (are)_S 75 _t (very)_S 76 _t (complex,)_S 75 _t (but)_S 75 _t (decrease)_S 76 _t (the)_S 75 _t (number)_S 76 _t (of)_S 75 _t (function)_S 1620 5650 _m (evaluations.)_S 174 _t (However,)_S 87 _t (it)_S 87 _t (occasionally)_S 87 _t (works)_S 87 _t (better)_S 87 _t (with)_S 87 _t (bounded)_S 87 _t (problems)_S 87 _t (in)_S 87 _t (that)_S 87 _t (it)_S 88 _t (has)_S 87 _t (less)_S 1620 5450 _m (tendency)_S 93 _t (to)_S 92 _t (get)_S 92 _t (stuck)_S 92 _t (at)_S 93 _t (boundaries)_S 92 _t (because)_S 92 _t (the)_S 92 _t (inaccuracies)_S 92 _t (in)_S 93 _t (the)_S 92 _t (Jacobian)_S 92 _t (result)_S 92 _t (in)_S 92 _t (search)_S 1620 5250 _m (directions)_S 61 _t (which)_S 61 _t (don't)_S 61 _t (pull)_S 61 _t (toward)_S 61 _t (the)_S 61 _t (boundary)_S 61 _t (as)_S 61 _t (strongly.)_S 61 _t 1200 4850 _m (6.)_S 1620 4850 _m (The)_S 61 _t (Lee)_S 61 _t (and)_S 61 _t (Lee)_S 61 _t (\(1989\))_S 61 _t /Times-BoldR 550 _ff (quasi-Newton)_S 61 _t (method)_S /Times-RomanR 550 _ff 61 _t (is)_S 60 _t (generally)_S 61 _t (faster)_S 61 _t (than)_S 61 _t (Broyden's)_S 61 _t (\(1965\))_S 61 _t (method)_S 1620 4650 _m (although)_S 89 _t (it)_S 89 _t (does)_S 88 _t (require)_S 89 _t (extra)_S 89 _t /Times-ItalicR 550 _ff (O)_S /Times-RomanR 550 _ff (\(n)_S /Times-RomanR 330 _ff 4314 4725 _m (2)_S 4369 4725 _m /Times-RomanR 550 _ff 4369 4650 _m (\))_S 89 _t (operations)_S 89 _t (internally;)_S 88 _t (the)_S 89 _t (choice)_S 89 _t (for)_S 88 _t (OMEGA)_S 89 _t (does)_S 89 _t (affect)_S 1620 4450 _m (performance.)_S 122 _t (There)_S 61 _t (is)_S 61 _t (little)_S 61 _t (difference)_S 61 _t (in)_S 61 _t (robustness)_S 61 _t (between)_S 61 _t (the)_S 61 _t (two.)_S 122 _t 1200 4050 _m (7.)_S 1620 4050 _m /Times-BoldR 550 _ff (RATIOF)_S 42 _t (and)_S 42 _t (MINQNS)_S /Times-RomanR 550 _ff 42 _t (can)_S 42 _t (have)_S 42 _t (an)_S 43 _t (effect)_S 42 _t (on)_S 42 _t (performance)_S 42 _t (in)_S 42 _t /Times-BoldR 550 _ff (quasi-Newton)_S 42 _t (methods)_S /Times-RomanR 550 _ff (;)_S 42 _t (they)_S 42 _t (control)_S 1620 3850 _m (how)_S 50 _t (often)_S 50 _t (the)_S 50 _t (Jacobian)_S 50 _t (is)_S 50 _t (evaluated)_S 50 _t (explicitly.)_S 100 _t (Try)_S 50 _t (changing)_S 50 _t (RATIOF)_S 49 _t (by)_S 50 _t (\0150.05's)_S 50 _t (and)_S 50 _t (MINQNS)_S 50 _t (by)_S 1620 3650 _m (\0151's.)_S 122 _t (They)_S 61 _t (usually)_S 61 _t (won't)_S 61 _t (affect)_S 61 _t (whether)_S 61 _t (you)_S 61 _t (find)_S 61 _t (a)_S 61 _t (solution.)_S 61 _t 1200 3250 _m (8.)_S 1620 3250 _m (The)_S 57 _t (parameter)_S 57 _t /Times-BoldR 550 _ff (NARMIJ)_S /Times-RomanR 550 _ff 58 _t (is)_S 57 _t (usually)_S 57 _t (best)_S 57 _t (at)_S 57 _t (1.)_S 114 _t (Forcing)_S 57 _t (descent)_S 57 _t (at)_S 57 _t (each)_S 57 _t (step)_S 57 _t (\(by)_S 57 _t (setting)_S 57 _t (NARMIJ)_S 57 _t (to)_S 1620 3050 _m (MAXIT\))_S 71 _t (almost)_S 72 _t (always)_S 71 _t (will)_S 72 _t (slow)_S 71 _t (progress)_S 71 _t (and)_S 72 _t (usually)_S 71 _t (not)_S 72 _t (increase)_S 71 _t (robustness.)_S 143 _t (You)_S 71 _t (will)_S 72 _t (likely)_S 1620 2850 _m (make)_S 61 _t (slower,)_S 61 _t (steadier)_S 61 _t (progress)_S 61 _t (by)_S 61 _t (increasing)_S 61 _t (NARMIJ.)_S 1200 2450 _m (9.)_S 1620 2450 _m (The)_S 65 _t (parameter)_S 65 _t /Times-BoldR 550 _ff (ACPTCR)_S /Times-RomanR 550 _ff 65 _t (is)_S 66 _t (usually)_S 65 _t (best)_S 65 _t (at)_S 65 _t (12.)_S 130 _t (In)_S 65 _t (a)_S 65 _t (sense,)_S 65 _t (the)_S 65 _t (aim)_S 65 _t (is)_S 65 _t (to)_S 65 _t (accept)_S 65 _t (as)_S 65 _t (many)_S 65 _t (steps)_S 65 _t (as)_S 1620 2250 _m (possible)_S 56 _t (without)_S 56 _t (diverging)_S 56 _t (thus)_S 55 _t (having)_S 56 _t (two)_S 56 _t (step)_S 56 _t (acceptance)_S 56 _t (criteria,)_S 55 _t (i.e.,)_S 56 _t /Times-ItalicR 550 _ff (f)_S /Times-RomanR 550 _ff 56 _t (and)_S 56 _t (the)_S 56 _t (natural)_S 55 _t (objective)_S 1620 2050 _m (function,)_S 61 _t (increases)_S 61 _t (the)_S 61 _t (percentage)_S 61 _t (of)_S 61 _t (longer,)_S 61 _t (accepted)_S 61 _t (steps.)_S 244 _t 4886 1250 _m (-)_S 61 _t (12)_S 61 _t (-)_S _ep _bp /Times-RomanR 550 _ff 0 13200 10200 _ornt /_r { sflg {/_t {0 rmoveto}bdef /ron false def} { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse }bdef 1200 11850 _m (10.)_S 1620 11850 _m (If)_S 65 _t (the)_S 65 _t (program)_S 64 _t (is)_S 65 _t (stopping)_S 65 _t (prematurely)_S 65 _t (because)_S 65 _t (of)_S 65 _t (the)_S 64 _t (step)_S 65 _t (size)_S 65 _t (criterion,)_S 65 _t (try)_S 65 _t /Times-BoldR 550 _ff (changing)_S 65 _t (STOPCR)_S 1620 11650 _m (to)_S 59 _t (2)_S /Times-RomanR 550 _ff 59 _t (thus)_S 59 _t (only)_S 59 _t (allowing)_S 59 _t (stopping)_S 59 _t (on)_S 59 _t (the)_S 59 _t (basis)_S 58 _t (of)_S 59 _t (the)_S 59 _t (max-norm)_S 59 _t (of)_S 59 _t (the)_S 59 _t (functions)_S 59 _t (nearing)_S 59 _t (zero.)_S 118 _t (The)_S 1620 11450 _m (program)_S 63 _t (will)_S 63 _t (still)_S 64 _t (stop)_S 63 _t (if)_S 63 _t (it)_S 63 _t (gets)_S 64 _t (stuck)_S 63 _t (at)_S 63 _t (a)_S 63 _t (local)_S 63 _t (minimum)_S 63 _t (however)_S 63 _t (it)_S 64 _t (will)_S 63 _t (not)_S 63 _t (stop)_S 63 _t (prematurely)_S 63 _t (at)_S 1620 11250 _m ("flat")_S 61 _t (spots)_S 61 _t (in)_S 61 _t (the)_S 61 _t (objective)_S 61 _t (function.)_S 1200 10850 _m (11.)_S 1620 10850 _m (For)_S 71 _t (well-behaved)_S 71 _t (problems)_S 71 _t (there)_S 71 _t (is)_S 71 _t (little)_S 71 _t (advantage)_S 71 _t (in)_S 71 _t (calculating)_S 71 _t /Times-BoldR 550 _ff (analytical)_S 71 _t (Jacobians)_S /Times-RomanR 550 _ff 71 _t (or)_S 71 _t (using)_S 1620 10650 _m (central)_S 75 _t (differences)_S 75 _t (over)_S 74 _t (forward)_S 75 _t (differences.)_S 150 _t (Symbolic)_S 75 _t (differentiation)_S 75 _t (software)_S 75 _t (can)_S 75 _t (be)_S 75 _t (useful)_S 75 _t (in)_S 1620 10450 _m (generating)_S 61 _t (analytical)_S 61 _t (derivatives)_S 61 _t (if)_S 61 _t (they)_S 61 _t (are)_S 61 _t (desired.)_S 1200 10050 _m (12.)_S 1620 10050 _m /Times-BoldR 550 _ff (OVERCH)_S /Times-RomanR 550 _ff 59 _t (may)_S 59 _t (save)_S 60 _t (problems)_S 59 _t (that)_S 59 _t (are)_S 59 _t (just)_S 59 _t (overflowing.)_S 119 _t (Generally)_S 59 _t (it)_S 59 _t (just)_S 59 _t (delays)_S 59 _t (the)_S 60 _t (inevitable)_S 59 _t (as)_S 1620 9850 _m (divergence)_S 61 _t (has)_S 61 _t (set)_S 62 _t (in.)_S 122 _t (The)_S 61 _t (default)_S 62 _t (damped)_S 61 _t (Newton)_S 61 _t (method)_S 61 _t (is)_S 62 _t (the)_S 61 _t (least)_S 61 _t (likely)_S 61 _t (to)_S 61 _t (overflow)_S 62 _t (and)_S 61 _t (the)_S 1620 9650 _m (straight)_S 74 _t (Newton's)_S 73 _t (method)_S 74 _t (the)_S 73 _t (most)_S 74 _t (likely.)_S 147 _t (Use)_S 74 _t /Times-BoldR 550 _ff (OVERFL)_S /Times-RomanR 550 _ff 73 _t (in)_S 74 _t (the)_S 73 _t (function)_S 74 _t (subroutine)_S 73 _t (to)_S 74 _t (prevent)_S 1620 9450 _m (exceptions)_S 61 _t (such)_S 61 _t (as)_S 61 _t (divide)_S 61 _t (by)_S 61 _t (zero,)_S 61 _t (invalid)_S 61 _t (arguments)_S 61 _t (...)_S 61 _t (.)_S 1200 9050 _m (13.)_S 1620 9050 _m (If)_S 61 _t (you)_S 61 _t (are)_S 61 _t (getting)_S 61 _t (stuck)_S 61 _t (at)_S 61 _t (boundaries)_S 61 _t (try)_S 61 _t /Times-BoldR 550 _ff (reducing)_S 61 _t (CONFAC)_S /Times-RomanR 550 _ff 61 _t (by)_S 61 _t (0.05's)_S 61 _t (as)_S 61 _t (a)_S 61 _t (last)_S 61 _t (resort.)_S 61 _t 1200 8650 _m (14.)_S 1620 8650 _m /Times-BoldR 550 _ff (ALPHA)_S /Times-RomanR 550 _ff 80 _t (is)_S 79 _t (usually)_S 80 _t (fine)_S 79 _t (at)_S 80 _t (1.0E-4.)_S 159 _t (In)_S 79 _t (problems)_S 80 _t (with)_S 79 _t (very)_S 80 _t (steep)_S 79 _t (objective)_S 80 _t (functions,)_S 79 _t (thus)_S 80 _t (large)_S 1620 8450 _m (directional)_S 82 _t (derivatives,)_S 83 _t (ALPHA)_S 83 _t (can)_S 83 _t (be)_S 83 _t (reduced)_S 83 _t (to)_S 83 _t (near)_S 82 _t (0.)_S 166 _t (Increasing)_S 83 _t (ALPHA)_S 83 _t (probably)_S 83 _t (won't)_S 1620 8250 _m (matter.)_S 1200 7850 _m 61 _t 1200 7850 _m (15.)_S 1620 7850 _m (Within)_S 61 _t /Times-BoldR 550 _ff (line)_S 61 _t (search)_S 61 _t (methods)_S /Times-RomanR 550 _ff (,)_S 61 _t (in)_S 61 _t (terms)_S 61 _t (of)_S 61 _t (solving/not)_S 61 _t (solving)_S 61 _t (the)_S 61 _t (problem)_S 1620 7650 _m (\267)_S 2040 7650 _m (switching)_S 61 _t (GEOMS)_S 61 _t (to)_S 61 _t (FALSE)_S 61 _t (usually)_S 61 _t (has)_S 61 _t (little)_S 61 _t (effect)_S 1620 7450 _m (\267)_S 2040 7450 _m (switching)_S 61 _t (DEUFLH)_S 61 _t (to)_S 61 _t (FALSE)_S 61 _t (usually)_S 61 _t (has)_S 61 _t (little)_S 61 _t (effect)_S 1620 7250 _m (\267)_S 2040 7250 _m (changing)_S 61 _t (MAXNS)_S 61 _t (and)_S 61 _t (MAXQNS)_S 61 _t (usually)_S 61 _t (has)_S 61 _t (little)_S 61 _t (effect)_S 1620 7050 _m (\267)_S 2040 7050 _m (changing)_S 61 _t (SIGMA)_S 61 _t (from)_S 61 _t (0.5)_S 61 _t (usually)_S 61 _t (has)_S 61 _t (little)_S 61 _t (effect)_S 1620 6850 _m (\267)_S 2040 6850 _m (changing)_S 92 _t (LAM0)_S 91 _t (from)_S 92 _t (1.0)_S 91 _t (should)_S 92 _t (only)_S 91 _t (be)_S 92 _t (used)_S 92 _t (as)_S 91 _t (a)_S 92 _t (last)_S 91 _t (resort)_S 92 _t (as)_S 92 _t (it)_S 91 _t (slows)_S 92 _t (performance)_S 2040 6650 _m (dramatically.)_S 187 _t (Try)_S 93 _t (using)_S 94 _t (MSTPF,)_S 93 _t (bounds)_S 94 _t (or)_S 93 _t (checks)_S 94 _t (within)_S 93 _t (the)_S 94 _t (function)_S 94 _t (vector)_S 93 _t (to)_S 94 _t (avoid)_S 2040 6450 _m (undefined)_S 61 _t (regions.)_S 1620 6250 _m (All)_S 56 _t (of)_S 55 _t (these)_S 56 _t (parameters)_S 55 _t (affect)_S 56 _t (performance.)_S 111 _t (SIGMA)_S 55 _t (should)_S 56 _t (not)_S 55 _t (be)_S 56 _t (changed)_S 55 _t (dramatically)_S 56 _t (from)_S 55 _t (0.5.)_S 1620 6050 _m (As)_S 61 _t (you)_S 61 _t (near)_S 61 _t (0)_S 61 _t (or)_S 61 _t (1)_S 61 _t (performance)_S 61 _t (degrades)_S 61 _t (noticeably.)_S 1200 5650 _m (16.)_S 1620 5650 _m (Within)_S 61 _t /Times-BoldR 550 _ff (trust)_S 61 _t (region)_S 61 _t (methods)_S /Times-RomanR 550 _ff (,)_S 61 _t (in)_S 61 _t (terms)_S 61 _t (of)_S 61 _t (solving/not)_S 61 _t (solving)_S 61 _t (the)_S 61 _t (problem)_S 1620 5450 _m (\267)_S 2040 5450 _m (switching)_S 61 _t (CAUCHY)_S 61 _t (to)_S 61 _t (TRUE)_S 61 _t (usually)_S 61 _t (has)_S 61 _t (little)_S 61 _t (effect)_S 1620 5250 _m (\267)_S 2040 5250 _m (if)_S 61 _t (you)_S 61 _t (are)_S 61 _t (having)_S 61 _t (overflow)_S 61 _t (problems)_S 61 _t (at)_S 61 _t (the)_S 61 _t (first)_S 61 _t (step)_S 61 _t (try)_S 61 _t (setting)_S 61 _t (DELTA.)_S 122 _t (Look)_S 61 _t (at)_S 61 _t (a)_S 62 _t (detailed)_S 2040 5050 _m (output)_S 61 _t (to)_S 61 _t (see)_S 61 _t (what)_S 61 _t (the)_S 61 _t (DELTA)_S 61 _t (calculated)_S 61 _t (internally)_S 61 _t (is)_S 61 _t (then)_S 61 _t (take)_S 61 _t (some)_S 61 _t (fraction)_S 61 _t (of)_S 61 _t (that)_S 1620 4850 _m (\267)_S 2040 4850 _m (changing)_S 61 _t (MAXNS)_S 61 _t (and)_S 61 _t (MAXQNS)_S 61 _t (usually)_S 61 _t (has)_S 61 _t (little)_S 61 _t (effect)_S 1620 4650 _m (\267)_S 2040 4650 _m (DELFAC)_S 63 _t (has)_S 62 _t (a)_S 63 _t (more)_S 62 _t (pronounced)_S 62 _t (effect)_S 62 _t (when)_S 63 _t (using)_S 62 _t (Dennis)_S 62 _t (and)_S 63 _t (Schnabel's)_S 62 _t (\(1983\))_S 62 _t (updating)_S 2040 4450 _m (method.)_S 84 _t (For)_S 43 _t (difficult)_S 42 _t (problems,)_S 42 _t (or)_S 42 _t (those)_S 43 _t (with)_S 42 _t (multiple)_S 42 _t (solutions,)_S 42 _t (changing)_S 42 _t (DELFAC)_S 43 _t (can)_S 42 _t (affect)_S 2040 4250 _m (what)_S 61 _t (solution)_S 61 _t (is)_S 61 _t (found.)_S 1620 4050 _m (\267)_S 2040 4050 _m (ETAFAC)_S 71 _t (can)_S 72 _t (be)_S 71 _t (increased)_S 71 _t (towards)_S 72 _t (1.)_S 142 _t (This)_S 71 _t (increases)_S 72 _t (the)_S 71 _t (influence)_S 71 _t (of)_S 71 _t (the)_S 72 _t (steepest)_S 71 _t (descent)_S 2040 3850 _m (direction)_S 61 _t (and)_S 61 _t (thus)_S 61 _t (is)_S 61 _t (slightly)_S 61 _t (more)_S 61 _t (conservative.)_S 1200 3450 _m (17.)_S 1620 3450 _m (If)_S 71 _t /Times-BoldR 550 _ff (progress)_S 72 _t (is)_S 71 _t (slow)_S /Times-RomanR 550 _ff 71 _t (in)_S 72 _t (decreasing)_S 71 _t (the)_S 72 _t (objective)_S 71 _t (function,)_S 72 _t (check)_S 71 _t (to)_S 72 _t (see)_S 71 _t (if)_S 71 _t (the)_S 72 _t (Jacobian)_S 71 _t (is)_S 72 _t (singular)_S 1620 3250 _m (using)_S 61 _t (detailed)_S 61 _t (output;)_S 61 _t (this)_S 61 _t (may)_S 61 _t (indicate)_S 61 _t (an)_S 61 _t (error)_S 61 _t (in)_S 61 _t (the)_S 61 _t (equations.)_S 1620 2850 _m (To)_S 64 _t (summarize,)_S 64 _t (try)_S 64 _t (changing)_S 64 _t (starting)_S 64 _t (points)_S 64 _t (and)_S 64 _t (methods)_S 64 _t (first.)_S 127 _t (Add)_S 64 _t (constraints)_S 64 _t (if)_S 64 _t (necessary.)_S 128 _t (The)_S 1200 2650 _m (trust)_S 50 _t (region)_S 50 _t (method)_S 49 _t (gives)_S 50 _t (more)_S 50 _t (flexibility.)_S 99 _t (For)_S 50 _t (line)_S 49 _t (search)_S 50 _t (methods)_S 49 _t (try)_S 50 _t (the)_S 50 _t (minimization)_S 49 _t (line)_S 50 _t (search.)_S 99 _t (Try)_S 1200 2450 _m (increasing)_S 50 _t (NARMIJ)_S 51 _t (and)_S 50 _t (changing)_S 50 _t (ACPTCR)_S 50 _t (to)_S 50 _t (1.)_S 101 _t (Rarely,)_S 50 _t (varying)_S 50 _t (the)_S 51 _t (parameters)_S 50 _t (listed)_S 50 _t (in)_S 50 _t (15)_S 51 _t (and)_S 50 _t (16)_S 50 _t (will)_S 1200 2250 _m (make)_S 56 _t (the)_S 55 _t (difference.)_S 111 _t (If)_S 56 _t (you)_S 55 _t (haven't)_S 55 _t (found)_S 56 _t (a)_S 55 _t (solution)_S 56 _t (yet,)_S 55 _t (you're)_S 55 _t (not)_S 56 _t (likely)_S 55 _t (to)_S 55 _t (using)_S 56 _t (NNES's)_S 55 _t (parameters.)_S 1200 2050 _m (A)_S 61 _t (few)_S 61 _t (suggestions)_S 61 _t (follow)_S 61 _t (which)_S 61 _t (still)_S 61 _t (might)_S 61 _t (help.)_S 4886 1250 _m (-)_S 61 _t (13)_S 61 _t (-)_S _ep _bp /Times-RomanR 550 _ff 0 13200 10200 _ornt /_r { sflg {/_t {0 rmoveto}bdef /ron false def} { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse }bdef 1200 11850 _m /Times-BoldR 550 _ff (2.3)_S 61 _t (Transforming)_S 61 _t (Problems)_S 61 _t (for)_S 61 _t (Easier)_S 61 _t (Solution)_S /Times-RomanR 550 _ff 1620 11450 _m (Transforming)_S 85 _t (the)_S 84 _t (problem)_S 85 _t (can)_S 85 _t (lead)_S 84 _t (to)_S 85 _t (easier)_S 85 _t (solution.)_S 169 _t (In)_S 85 _t (general,)_S 84 _t (the)_S 85 _t (objective)_S 85 _t (is)_S 84 _t (to)_S 85 _t (redefine)_S 1200 11250 _m (arguments)_S 55 _t (of)_S 56 _t (logarithms...)_S 55 _t (as)_S 55 _t (variables,)_S 55 _t (so)_S 56 _t (constraints)_S 55 _t (can)_S 55 _t (be)_S 56 _t (applied)_S 55 _t (to)_S 55 _t (these)_S 56 _t (variables,)_S 55 _t (and)_S 55 _t (to)_S 55 _t (transform)_S 1200 11050 _m (highly)_S 61 _t (nonlinear)_S 61 _t (functions)_S 61 _t (such)_S 61 _t (as)_S 61 _t (exponentials)_S 61 _t (and)_S 61 _t (high-order)_S 61 _t (polynomials.)_S 1620 10650 _m (Consider)_S 75 _t (these)_S 75 _t (two)_S 75 _t (examples)_S 75 _t (from)_S 75 _t (Shacham)_S 75 _t (\(1983\))_S 75 _t (and)_S 75 _t (\(1986\).)_S 151 _t (The)_S 75 _t (first)_S 75 _t (is)_S 75 _t (a)_S 75 _t (one-dimensional)_S 1200 10450 _m (problem)_S 60 _t (which)_S 61 _t (has)_S 60 _t (an)_S 61 _t (infeasible)_S 60 _t (range)_S 61 _t (of)_S 60 _t ([.8,1].)_S 121 _t (The)_S 61 _t (initial)_S 60 _t (estimate)_S 61 _t (is)_S 60 _t (0.5)_S 61 _t (and)_S 60 _t (there)_S 61 _t (are)_S 60 _t (two)_S 61 _t (solutions:)_S 1200 10250 _m (0.7574)_S 61 _t (\(feasible\))_S 61 _t (and)_S 61 _t (1.098)_S 61 _t (\(infeasible\).)_S 1620 9850 _m (F\(x\))_S 61 _t (=)_S 61 _t (x/\(1)_S 61 _t (-)_S 61 _t (x\))_S 61 _t (-)_S 61 _t (5ln[0.4\(1)_S 61 _t (-)_S 61 _t (x\)/\(0.4)_S 61 _t (-)_S 61 _t (0.5x\)])_S 61 _t (+)_S 61 _t (4.45977)_S 61 _t (=)_S 61 _t (0)_S 244 _t (x)_S 61 _t /Symbol 550 _ff (\243)_S /Times-RomanR 550 _ff 61 _t (1)_S 1200 9450 _m (This)_S 61 _t (1-dimensional)_S 61 _t (problem)_S 61 _t (can)_S 61 _t (be)_S 61 _t (transformed)_S 61 _t (into)_S 61 _t (the)_S 61 _t (following)_S 61 _t (3-dimensional)_S 61 _t (system:)_S 1620 9050 _m (x)_S /Times-RomanR 330 _ff 1712 9009 _m (1)_S 1767 9009 _m /Times-RomanR 550 _ff 1767 9050 _m 61 _t (=)_S 61 _t (x)_S 1620 8850 _m (x)_S /Times-RomanR 330 _ff 1712 8809 _m (2)_S 1767 8809 _m /Times-RomanR 550 _ff 1767 8850 _m 61 _t (=)_S 61 _t (1)_S 61 _t (-)_S 61 _t (x)_S 1620 8650 _m (x)_S /Times-RomanR 330 _ff 1712 8609 _m (3)_S 1767 8609 _m /Times-RomanR 550 _ff 1767 8650 _m 61 _t (=)_S 61 _t (0.5x)_S 61 _t (-)_S 61 _t (0.4)_S 1620 8250 _m (F)_S /Times-RomanR 330 _ff 1722 8209 _m (1)_S 1777 8209 _m /Times-RomanR 550 _ff 1777 8250 _m (\()_S /Times-BoldR 550 _ff (x)_S /Times-RomanR 550 _ff (\))_S 61 _t (=)_S 61 _t (x)_S /Times-RomanR 330 _ff 2308 8209 _m (1)_S 2363 8209 _m /Times-RomanR 550 _ff 2363 8250 _m (/x)_S /Times-RomanR 330 _ff 2505 8209 _m (2)_S 2560 8209 _m /Times-RomanR 550 _ff 2560 8250 _m 61 _t (-)_S 61 _t (5ln\(0.4x)_S /Times-RomanR 330 _ff 3360 8209 _m (2)_S 3415 8209 _m /Times-RomanR 550 _ff 3415 8250 _m (/x)_S /Times-RomanR 330 _ff 3557 8209 _m (3)_S 3612 8209 _m /Times-RomanR 550 _ff 3612 8250 _m (\))_S 61 _t (+)_S 61 _t (4.45977)_S 61 _t (=)_S 61 _t (0)_S 1620 8050 _m (F)_S /Times-RomanR 330 _ff 1722 8009 _m (2)_S 1777 8009 _m /Times-RomanR 550 _ff 1777 8050 _m (\()_S /Times-BoldR 550 _ff (x)_S /Times-RomanR 550 _ff (\))_S 61 _t (=)_S 61 _t (x)_S /Times-RomanR 330 _ff 2308 8009 _m (1)_S 2363 8009 _m /Times-RomanR 550 _ff 2363 8050 _m 61 _t (+)_S 61 _t (x)_S /Times-RomanR 330 _ff 2680 8009 _m (2)_S 2735 8009 _m /Times-RomanR 550 _ff 2735 8050 _m 61 _t (-)_S 61 _t (1)_S 61 _t (=)_S 61 _t (0)_S 1620 7850 _m (F)_S /Times-RomanR 330 _ff 1722 7809 _m (3)_S 1777 7809 _m /Times-RomanR 550 _ff 1777 7850 _m (\()_S /Times-BoldR 550 _ff (x)_S /Times-RomanR 550 _ff (\))_S 61 _t (=)_S 61 _t (0.5x)_S /Times-RomanR 330 _ff 2537 7809 _m (1)_S 2592 7809 _m /Times-RomanR 550 _ff 2592 7850 _m 61 _t (+)_S 61 _t (x)_S /Times-RomanR 330 _ff 2909 7809 _m (3)_S 2964 7809 _m /Times-RomanR 550 _ff 2964 7850 _m 61 _t (-)_S 61 _t (0.4)_S 61 _t (=)_S 61 _t (0)_S 1200 7450 _m (which)_S 51 _t (has)_S 50 _t (the)_S 51 _t (limits:)_S 51 _t (x)_S /Times-RomanR 330 _ff 2880 7409 _m (1)_S 2935 7409 _m /Times-RomanR 550 _ff 2935 7450 _m 51 _t /Symbol 550 _ff (\263)_S /Times-RomanR 550 _ff 50 _t (0;)_S 51 _t (x)_S /Times-RomanR 330 _ff 3422 7409 _m (2)_S 3477 7409 _m /Times-RomanR 550 _ff 3477 7450 _m 51 _t (>)_S 50 _t (0)_S 51 _t (and)_S 51 _t (x)_S /Times-RomanR 330 _ff 4231 7409 _m (3)_S 4286 7409 _m /Times-RomanR 550 _ff 4286 7450 _m 51 _t (>)_S 50 _t (0)_S 51 _t (which)_S 51 _t (are)_S 50 _t (continuous)_S 51 _t (in)_S 51 _t (these)_S 51 _t (ranges)_S 50 _t (and)_S 51 _t (force)_S 51 _t (the)_S 50 _t (original)_S 1200 7250 _m (x)_S 61 _t (to)_S 61 _t (be)_S 61 _t /Symbol 550 _ff (\243)_S /Times-RomanR 550 _ff 61 _t (1)_S 61 _t (thus)_S 61 _t (implying)_S 61 _t (its)_S 61 _t (feasibility.)_S 1620 6850 _m (The)_S 74 _t (second)_S 74 _t (example)_S 73 _t (involves)_S 74 _t (redefining)_S 73 _t (variables)_S 74 _t (plus)_S 73 _t (transforming)_S 74 _t (the)_S 74 _t (first)_S 73 _t (equation)_S 74 _t (by)_S 73 _t (taking)_S 1200 6650 _m (logarithms.)_S 122 _t (The)_S 61 _t (original)_S 61 _t (version)_S 61 _t (is)_S 1620 6250 _m (F)_S /Times-RomanR 330 _ff 1722 6209 _m (1)_S 1777 6209 _m /Times-RomanR 550 _ff 1777 6250 _m (\()_S /Times-BoldR 550 _ff (x)_S /Times-RomanR 550 _ff (\))_S 61 _t (=)_S 61 _t (120x)_S /Times-RomanR 330 _ff 2583 6209 _m (1)_S 2638 6209 _m /Times-RomanR 550 _ff 2638 6250 _m 61 _t (-)_S 61 _t (75k\(1)_S 61 _t (-)_S 61 _t (x)_S /Times-RomanR 330 _ff 3523 6209 _m (1)_S 3578 6209 _m /Times-RomanR 550 _ff 3578 6250 _m (\))_S 61 _t (=)_S 61 _t (0)_S 1620 6050 _m (F)_S /Times-RomanR 330 _ff 1722 6009 _m (2)_S 1777 6009 _m /Times-RomanR 550 _ff 1777 6050 _m (\()_S /Times-BoldR 550 _ff (x)_S /Times-RomanR 550 _ff (\))_S 61 _t (=)_S 61 _t (x)_S /Times-RomanR 330 _ff 2308 6009 _m (1)_S 2363 6009 _m /Times-RomanR 550 _ff 2363 6050 _m (\(873)_S 61 _t (-)_S 61 _t (x)_S /Times-RomanR 330 _ff 2974 6009 _m (2)_S 3029 6009 _m /Times-RomanR 550 _ff 3029 6050 _m (\))_S 61 _t (-)_S 61 _t (11\(x)_S /Times-RomanR 330 _ff 3609 6009 _m (2)_S 3664 6009 _m /Times-RomanR 550 _ff 3664 6050 _m 61 _t (-)_S 61 _t (300\))_S 61 _t (=)_S 61 _t (0)_S 1620 5650 _m (where)_S 183 _t (k)_S 61 _t (=)_S 61 _t (0.12exp[12581\(x)_S /Times-RomanR 330 _ff 3826 5609 _m (2)_S 3881 5609 _m /Times-RomanR 550 _ff 3881 5650 _m 61 _t (-)_S 61 _t (298\)/\(298x)_S /Times-RomanR 330 _ff 4878 5609 _m (2)_S 4933 5609 _m /Times-RomanR 550 _ff 4933 5650 _m (\)])_S 1200 5250 _m (while)_S 61 _t (the)_S 61 _t (modified)_S 61 _t (problem,)_S 61 _t (which)_S 61 _t (no)_S 61 _t (longer)_S 61 _t (has)_S 61 _t (the)_S 61 _t (highly)_S 61 _t (nonlinear)_S 61 _t (exponential)_S 61 _t (term,)_S 61 _t (is)_S 1620 4850 _m (x)_S /Times-RomanR 330 _ff 1712 4809 _m (3)_S 1767 4809 _m /Times-RomanR 550 _ff 1767 4850 _m 61 _t (=)_S 61 _t (\(1)_S 61 _t (-)_S 61 _t (x)_S /Times-RomanR 330 _ff 2420 4809 _m (1)_S 2475 4809 _m /Times-RomanR 550 _ff 2475 4850 _m (\)/x)_S /Times-RomanR 330 _ff 2678 4809 _m (1)_S /Times-RomanR 550 _ff 1620 4450 _m (F)_S /Times-RomanR 330 _ff 1722 4409 _m (1)_S 1777 4409 _m /Times-RomanR 550 _ff 1777 4450 _m (\()_S /Times-BoldR 550 _ff (x)_S /Times-RomanR 550 _ff (\))_S 61 _t (=)_S 61 _t (ln\(40/3x)_S /Times-RomanR 330 _ff 2837 4409 _m (3)_S 2892 4409 _m /Times-RomanR 550 _ff 2892 4450 _m (\))_S 61 _t (-)_S 61 _t ([12581\(x)_S /Times-RomanR 330 _ff 3809 4409 _m (2)_S 3864 4409 _m /Times-RomanR 550 _ff 3864 4450 _m 61 _t (-)_S 61 _t (298\)/\(298x)_S /Times-RomanR 330 _ff 4861 4409 _m (2)_S 4916 4409 _m /Times-RomanR 550 _ff 4916 4450 _m (\)])_S 61 _t (=)_S 61 _t (0)_S 61 _t 1620 4250 _m (F)_S /Times-RomanR 330 _ff 1722 4209 _m (2)_S 1777 4209 _m /Times-RomanR 550 _ff 1777 4250 _m (\()_S /Times-BoldR 550 _ff (x)_S /Times-RomanR 550 _ff (\))_S 61 _t (=)_S 61 _t (x)_S /Times-RomanR 330 _ff 2308 4209 _m (1)_S 2363 4209 _m /Times-RomanR 550 _ff 2363 4250 _m (\(873)_S 61 _t (-)_S 61 _t (x)_S /Times-RomanR 330 _ff 2974 4209 _m (2)_S 3029 4209 _m /Times-RomanR 550 _ff 3029 4250 _m (\))_S 61 _t (-)_S 61 _t (11\(x)_S /Times-RomanR 330 _ff 3609 4209 _m (2)_S 3664 4209 _m /Times-RomanR 550 _ff 3664 4250 _m (-300\))_S 61 _t (=)_S 61 _t (0)_S 1620 4050 _m (F)_S /Times-RomanR 330 _ff 1722 4009 _m (3)_S 1777 4009 _m /Times-RomanR 550 _ff 1777 4050 _m (\()_S /Times-BoldR 550 _ff (x)_S /Times-RomanR 550 _ff (\))_S 61 _t (=)_S 61 _t (\(1)_S 61 _t (-)_S 61 _t (x)_S /Times-RomanR 330 _ff 2644 4009 _m (1)_S 2699 4009 _m /Times-RomanR 550 _ff 2699 4050 _m (\))_S 61 _t (-)_S 61 _t (x)_S /Times-RomanR 330 _ff 3034 4009 _m (3)_S 3089 4009 _m /Times-RomanR 550 _ff 3089 4050 _m (x)_S /Times-RomanR 330 _ff 3181 4009 _m (1)_S 3236 4009 _m /Times-RomanR 550 _ff 3236 4050 _m 61 _t (=)_S 61 _t (0)_S 1200 3650 _m (which)_S 71 _t (has)_S 70 _t (the)_S 71 _t (limit)_S 71 _t (x)_S /Times-RomanR 330 _ff 2838 3609 _m (3)_S 2893 3609 _m /Times-RomanR 550 _ff 2893 3650 _m 71 _t (>)_S 71 _t (0.)_S 142 _t (Notice)_S 71 _t (that)_S 71 _t (the)_S 71 _t (second)_S 71 _t (equation)_S 71 _t (has)_S 71 _t (remained)_S 71 _t (unchanged.)_S 142 _t (For)_S 71 _t (the)_S 71 _t (initial)_S 1200 3450 _m (estimates)_S 54 _t (of)_S 54 _t (\(0.5,320\),)_S 54 _t (NNES)_S 54 _t (fails)_S 54 _t (for)_S 53 _t (the)_S 54 _t (original)_S 54 _t (formulation)_S 54 _t (but)_S 54 _t (using,)_S 54 _t (for)_S 54 _t (example,)_S 54 _t (an)_S 54 _t (initial)_S 54 _t (estimate)_S 1200 3250 _m (of)_S 83 _t (0.1)_S 83 _t (for)_S 82 _t (x)_S /Times-RomanR 330 _ff 2135 3209 _m (3)_S 2190 3209 _m /Times-RomanR 550 _ff 2190 3250 _m (,)_S 83 _t (converges)_S 83 _t (quickly)_S 82 _t (to)_S 83 _t (the)_S 83 _t (solution)_S 82 _t (\(0.96387,)_S 83 _t (346.16,)_S 83 _t (0.0374\).)_S 165 _t (The)_S 83 _t (value)_S 82 _t (of)_S 83 _t (x)_S /Times-RomanR 330 _ff 8352 3209 _m (3)_S 8407 3209 _m /Times-RomanR 550 _ff 8407 3250 _m 83 _t (has)_S 82 _t (no)_S 1200 3050 _m (meaning)_S 61 _t (but)_S 61 _t (the)_S 61 _t (first)_S 61 _t (two)_S 61 _t (entries)_S 61 _t (are)_S 61 _t (the)_S 61 _t (correct)_S 61 _t (solution)_S 61 _t (to)_S 61 _t (the)_S 61 _t (original)_S 61 _t (problem.)_S 1620 2650 _m (Another)_S 62 _t (way)_S 62 _t (to)_S 62 _t (reparameterize)_S 62 _t (is)_S 62 _t (to)_S 62 _t (change)_S 62 _t (the)_S 62 _t (variables.)_S 124 _t (The)_S 62 _t (most)_S 62 _t (common)_S 62 _t (transformations)_S 62 _t (are)_S 1200 2450 _m (to)_S 60 _t (use)_S 59 _t (logarithms)_S 60 _t (and)_S 60 _t (powers)_S 59 _t (of)_S 60 _t (the)_S 60 _t (original)_S 60 _t (variables)_S 59 _t (as)_S 60 _t (new)_S 60 _t (variables.)_S 119 _t (For)_S 60 _t (example,)_S 60 _t (use)_S 59 _t (x)_S /Times-RomanR 330 _ff 8153 2525 _m (2)_S 8208 2525 _m /Times-RomanR 550 _ff 8208 2450 _m 60 _t (instead)_S 60 _t (of)_S 1200 2250 _m (x)_S 72 _t (to)_S 72 _t (ensure)_S 73 _t (nonnegativity.)_S 144 _t (Transforming)_S 72 _t (in)_S 72 _t (this)_S 73 _t (manner)_S 72 _t (may)_S 72 _t (cause)_S 72 _t (linear)_S 72 _t (terms)_S 73 _t (in)_S 72 _t (other)_S 72 _t (equations)_S 72 _t (to)_S 1200 2050 _m (become)_S 61 _t (nonlinear)_S 61 _t (so)_S 61 _t (the)_S 61 _t (trade-offs)_S 61 _t (must)_S 61 _t (be)_S 61 _t (examined.)_S 4886 1250 _m (-)_S 61 _t (14)_S 61 _t (-)_S _ep _bp /Times-RomanR 550 _ff 0 13200 10200 _ornt /_r { sflg {/_t {0 rmoveto}bdef /ron false def} { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse }bdef 1620 11850 _m (Consider)_S 61 _t (equations)_S 61 _t (of)_S 61 _t (the)_S 61 _t (following)_S 61 _t (form)_S 61 _t (with)_S 61 _t (starting)_S 61 _t (estimate)_S 61 _t (\(1,1\):)_S 1620 11450 _m (F)_S /Times-RomanR 330 _ff 1722 11409 _m (1)_S 1777 11409 _m /Times-RomanR 550 _ff 1777 11450 _m (\()_S /Times-BoldR 550 _ff (x)_S /Times-RomanR 550 _ff (\))_S 61 _t (=)_S 61 _t (x)_S /Times-RomanR 330 _ff 2308 11409 _m (1)_S 2363 11409 _m /Times-RomanR 550 _ff 2363 11450 _m (x)_S /Times-RomanR 330 _ff 2454 11409 _m (2)_S 2509 11450 _m 2509 11525 _m (1/2)_S 2650 11525 _m /Times-RomanR 550 _ff 2650 11450 _m 61 _t (-)_S 61 _t (2x)_S /Times-RomanR 330 _ff 3016 11409 _m (1)_S 3071 11409 _m /Times-RomanR 550 _ff 3071 11450 _m 61 _t (-)_S 61 _t (3)_S 61 _t (=)_S 61 _t (0)_S 1620 11250 _m (F)_S /Times-RomanR 330 _ff 1722 11209 _m (2)_S 1777 11209 _m /Times-RomanR 550 _ff 1777 11250 _m (\()_S /Times-BoldR 550 _ff (x)_S /Times-RomanR 550 _ff (\))_S 61 _t (=)_S 61 _t (\(1)_S 61 _t (+)_S 61 _t (x)_S /Times-RomanR 330 _ff 2686 11209 _m (2)_S 2741 11209 _m /Times-RomanR 550 _ff 2741 11250 _m (\)x)_S /Times-RomanR 330 _ff 2894 11209 _m (1)_S 2949 11209 _m /Times-RomanR 550 _ff 2949 11250 _m 61 _t (+)_S 61 _t (3)_S 61 _t (=)_S 61 _t (0)_S 1620 10850 _m (The)_S 47 _t (square)_S 47 _t (root)_S 47 _t (in)_S 46 _t (the)_S 47 _t (first)_S 47 _t (equation)_S 47 _t (causes)_S 47 _t (an)_S 46 _t (error)_S 47 _t (at)_S 47 _t (the)_S 46 _t (second)_S 47 _t (step)_S 47 _t (when)_S 47 _t (using)_S 47 _t (the)_S 46 _t (default)_S 47 _t (setting)_S 1200 10650 _m (in)_S 52 _t (NNES.)_S 102 _t (This)_S 52 _t (can)_S 51 _t (be)_S 52 _t (averted)_S 51 _t (by)_S 51 _t (using)_S 52 _t (a)_S 51 _t (lower)_S 52 _t (bound)_S 51 _t (of)_S 51 _t (0)_S 52 _t (for)_S 51 _t (x)_S /Times-RomanR 330 _ff 6019 10609 _m (2)_S 6074 10609 _m /Times-RomanR 550 _ff 6074 10650 _m 51 _t (but)_S 52 _t (one)_S 51 _t (could)_S 52 _t (also)_S 51 _t (modify)_S 52 _t (the)_S 51 _t (problem)_S 1200 10450 _m (by)_S 61 _t (defining)_S 61 _t (a)_S 61 _t (new)_S 61 _t (variable)_S 61 _t (x)_S /Times-RomanR 330 _ff 3368 10409 _m (3)_S 3423 10409 _m /Times-RomanR 550 _ff 3423 10450 _m 61 _t (=)_S 61 _t (x)_S /Times-RomanR 330 _ff 3740 10409 _m (2)_S 3795 10450 _m 3795 10525 _m (1/2)_S 3936 10525 _m /Times-RomanR 550 _ff 3936 10450 _m 61 _t (to)_S 1620 10050 _m (F)_S /Times-RomanR 330 _ff 1722 10009 _m (1)_S 1777 10009 _m /Times-RomanR 550 _ff 1777 10050 _m (\()_S /Times-BoldR 550 _ff (x)_S /Times-RomanR 550 _ff (\))_S 61 _t (=)_S 61 _t (x)_S /Times-RomanR 330 _ff 2308 10009 _m (1)_S 2363 10009 _m /Times-RomanR 550 _ff 2363 10050 _m (x)_S /Times-RomanR 330 _ff 2454 10009 _m (3)_S 2509 10009 _m /Times-RomanR 550 _ff 2509 10050 _m 61 _t (-)_S 61 _t (2x)_S /Times-RomanR 330 _ff 2876 10009 _m (1)_S 2931 10009 _m /Times-RomanR 550 _ff 2931 10050 _m 61 _t (-)_S 61 _t (3)_S 61 _t (=)_S 61 _t (0)_S 1620 9850 _m (F)_S /Times-RomanR 330 _ff 1722 9809 _m (2)_S 1777 9809 _m /Times-RomanR 550 _ff 1777 9850 _m (\()_S /Times-BoldR 550 _ff (x)_S /Times-RomanR 550 _ff (\))_S 61 _t (=)_S 61 _t (\(1)_S 61 _t (+)_S 61 _t (x)_S /Times-RomanR 330 _ff 2686 9809 _m (3)_S 2741 9850 _m 2741 9925 _m (2)_S 2796 9925 _m /Times-RomanR 550 _ff 2796 9850 _m (\)x)_S /Times-RomanR 330 _ff 2949 9809 _m (1)_S 3004 9809 _m /Times-RomanR 550 _ff 3004 9850 _m 61 _t (+)_S 61 _t (3)_S 61 _t (=)_S 61 _t (0)_S 1200 9450 _m (which)_S 58 _t (is)_S 57 _t (easily)_S 58 _t (solved)_S 57 _t (to)_S 57 _t (give)_S 57 _t (the)_S 58 _t (solution)_S 57 _t (\(-2.1708,)_S 57 _t (0.6180\))_S 58 _t (so)_S 57 _t (the)_S 57 _t (solution)_S 58 _t (of)_S 57 _t (the)_S 57 _t (original)_S 58 _t (problem)_S 57 _t (is)_S 57 _t (\(-)_S 1200 9250 _m (2.1708,)_S 61 _t (0.3820\).)_S 1200 8850 _m /Times-BoldR 550 _ff (2.4)_S 61 _t (Using)_S 61 _t (Other)_S 61 _t (Methods)_S /Times-RomanR 550 _ff 1620 8450 _m (Another)_S 79 _t (possibility)_S 79 _t (is)_S 79 _t (to)_S 78 _t (use)_S 79 _t (the)_S 79 _t (a)_S 79 _t (form)_S 79 _t (of)_S 79 _t (the)_S 79 _t (continuation)_S 78 _t (method.)_S 158 _t (NNES)_S 79 _t (is)_S 79 _t (not)_S 79 _t (set)_S 79 _t (up)_S 78 _t (as)_S 79 _t (a)_S 1200 8250 _m (continuation)_S 53 _t (method)_S 53 _t (but)_S 53 _t (a)_S 52 _t (version)_S 53 _t (can)_S 53 _t (be)_S 53 _t (developed)_S 53 _t (using)_S 53 _t (NNES)_S 53 _t (as)_S 53 _t (the)_S 52 _t (core.)_S 106 _t (The)_S 53 _t (objective)_S 53 _t (is)_S 53 _t (to)_S 53 _t (choose)_S 1200 8050 _m (a)_S 75 _t (continuation)_S 74 _t (parameter,)_S 75 _t (some)_S 75 _t (variable)_S 75 _t _U (in)_S _u 75 _t (the)_S 75 _t (problem)_S 75 _t (which)_S 75 _t (is)_S 75 _t (causing)_S 75 _t (the)_S 75 _t (severe)_S 75 _t (nonlinearity,)_S 75 _t (and)_S 1200 7850 _m (transform)_S 57 _t (it)_S 58 _t (in)_S 57 _t (several)_S 57 _t (stages)_S 58 _t (from)_S 57 _t (a)_S 58 _t (level)_S 57 _t (where)_S 57 _t (the)_S 58 _t (system)_S 57 _t (is)_S 58 _t (more)_S 57 _t (readily)_S 57 _t (solvable)_S 58 _t (to)_S 57 _t (its)_S 58 _t (desired)_S 57 _t (level.)_S 1200 7650 _m (As)_S 61 _t (an)_S 61 _t (illustration,)_S 61 _t (consider)_S 61 _t (Hiebert's)_S 61 _t (\(1980\))_S 61 _t (2)_S /Times-RomanR 330 _ff 4667 7725 _m (nd)_S 4777 7725 _m /Times-RomanR 550 _ff 4777 7650 _m 61 _t (chemical)_S 61 _t (engineering)_S 61 _t (problem:)_S 1620 7250 _m (F)_S /Times-RomanR 330 _ff 1722 7209 _m (1)_S 1777 7209 _m /Times-RomanR 550 _ff 1777 7250 _m (\()_S /Times-BoldR 550 _ff (x)_S /Times-RomanR 550 _ff (\))_S 61 _t (=)_S 61 _t (x)_S /Times-RomanR 330 _ff 2308 7209 _m (1)_S 2363 7209 _m /Times-RomanR 550 _ff 2363 7250 _m 61 _t (+)_S 61 _t (x)_S /Times-RomanR 330 _ff 2680 7209 _m (2)_S 2735 7209 _m /Times-RomanR 550 _ff 2735 7250 _m 61 _t (+)_S 61 _t (x)_S /Times-RomanR 330 _ff 3052 7209 _m (4)_S 3107 7209 _m /Times-RomanR 550 _ff 3107 7250 _m 61 _t (-)_S 61 _t (0.001)_S 61 _t (=)_S 61 _t (0)_S 1620 7050 _m (F)_S /Times-RomanR 330 _ff 1722 7009 _m (2)_S 1777 7009 _m /Times-RomanR 550 _ff 1777 7050 _m (\()_S /Times-BoldR 550 _ff (x)_S /Times-RomanR 550 _ff (\))_S 61 _t (=)_S 61 _t (x)_S /Times-RomanR 330 _ff 2308 7009 _m (5)_S 2363 7009 _m /Times-RomanR 550 _ff 2363 7050 _m 61 _t (+)_S 61 _t (x)_S /Times-RomanR 330 _ff 2680 7009 _m (6)_S 2735 7009 _m /Times-RomanR 550 _ff 2735 7050 _m 61 _t (-)_S 61 _t (55.0)_S 61 _t (=)_S 61 _t (0)_S 1620 6850 _m (F)_S /Times-RomanR 330 _ff 1722 6809 _m (3)_S 1777 6809 _m /Times-RomanR 550 _ff 1777 6850 _m (\()_S /Times-BoldR 550 _ff (x)_S /Times-RomanR 550 _ff (\))_S 61 _t (=)_S 61 _t (x)_S /Times-RomanR 330 _ff 2308 6809 _m (1)_S 2363 6809 _m /Times-RomanR 550 _ff 2363 6850 _m 61 _t (+)_S 61 _t (x)_S /Times-RomanR 330 _ff 2680 6809 _m (2)_S 2735 6809 _m /Times-RomanR 550 _ff 2735 6850 _m 61 _t (+)_S 61 _t (x)_S /Times-RomanR 330 _ff 3052 6809 _m (3)_S 3107 6809 _m /Times-RomanR 550 _ff 3107 6850 _m 61 _t (+)_S 61 _t (2x)_S /Times-RomanR 330 _ff 3516 6809 _m (5)_S 3571 6809 _m /Times-RomanR 550 _ff 3571 6850 _m 61 _t (+)_S 61 _t (x)_S /Times-RomanR 330 _ff 3888 6809 _m (6)_S 3943 6809 _m /Times-RomanR 550 _ff 3943 6850 _m 61 _t (-)_S 61 _t (110.001)_S 61 _t (=)_S 61 _t (0)_S 1620 6650 _m (F)_S /Times-RomanR 330 _ff 1722 6609 _m (4)_S 1777 6609 _m /Times-RomanR 550 _ff 1777 6650 _m (\()_S /Times-BoldR 550 _ff (x)_S /Times-RomanR 550 _ff (\))_S 61 _t (=)_S 61 _t (x)_S /Times-RomanR 330 _ff 2308 6609 _m (1)_S 2363 6609 _m /Times-RomanR 550 _ff 2363 6650 _m 61 _t (-)_S 61 _t (0.1x)_S /Times-RomanR 330 _ff 2867 6609 _m (2)_S 2922 6609 _m /Times-RomanR 550 _ff 2922 6650 _m 61 _t (=)_S 61 _t (0)_S 1620 6450 _m (F)_S /Times-RomanR 330 _ff 1722 6409 _m (5)_S 1777 6409 _m /Times-RomanR 550 _ff 1777 6450 _m (\()_S /Times-BoldR 550 _ff (x)_S /Times-RomanR 550 _ff (\))_S 61 _t (=)_S 61 _t (x)_S /Times-RomanR 330 _ff 2308 6409 _m (1)_S 2363 6409 _m /Times-RomanR 550 _ff 2363 6450 _m 61 _t (-)_S 61 _t (10000.0x)_S /Times-RomanR 330 _ff 3233 6409 _m (3)_S 3288 6409 _m /Times-RomanR 550 _ff 3288 6450 _m (x)_S /Times-RomanR 330 _ff 3380 6409 _m (4)_S 3435 6409 _m /Times-RomanR 550 _ff 3435 6450 _m 61 _t (=)_S 61 _t (0)_S 1620 6250 _m (F)_S /Times-RomanR 330 _ff 1722 6209 _m (6)_S 1777 6209 _m /Times-RomanR 550 _ff 1777 6250 _m (\()_S /Times-BoldR 550 _ff (x)_S /Times-RomanR 550 _ff (\))_S 61 _t (=)_S 61 _t (x)_S /Times-RomanR 330 _ff 2308 6209 _m (5)_S 2363 6209 _m /Times-RomanR 550 _ff 2363 6250 _m 61 _t (-)_S 61 _t (5.5\00310)_S /Times-RomanR 330 _ff 3062 6325 _m (15)_S 3172 6325 _m /Times-RomanR 550 _ff 3172 6250 _m (x)_S /Times-RomanR 330 _ff 3263 6209 _m (3)_S 3318 6209 _m /Times-RomanR 550 _ff 3318 6250 _m (x)_S /Times-RomanR 330 _ff 3410 6209 _m (6)_S 3465 6209 _m /Times-RomanR 550 _ff 3465 6250 _m 61 _t (=)_S 61 _t (0)_S 1200 5850 _m (which)_S 64 _t (is)_S 64 _t (very)_S 63 _t (badly)_S 64 _t (scaled)_S 64 _t (because)_S 63 _t (of)_S 64 _t (the)_S 63 _t (10)_S /Times-RomanR 330 _ff 4611 5925 _m (15)_S 4721 5925 _m /Times-RomanR 550 _ff 4721 5850 _m 64 _t (in)_S 64 _t (the)_S 63 _t (last)_S 64 _t (equation.)_S 127 _t (One)_S 64 _t (approach)_S 64 _t (would)_S 63 _t (be)_S 64 _t (to)_S 63 _t (replace)_S 1200 5650 _m (the)_S 64 _t (exponent)_S 65 _t (15)_S 64 _t (with)_S 65 _t (a)_S 64 _t (parameter,)_S 65 _t (call)_S 64 _t (it)_S 65 _t (K,)_S 64 _t (and)_S 65 _t (solve)_S 64 _t (a)_S 65 _t (series)_S 64 _t (of)_S 65 _t (problems)_S 64 _t (where)_S 65 _t (the)_S 64 _t (parameter)_S 65 _t (varies)_S 1200 5450 _m (from,)_S 47 _t (say)_S 46 _t (K=1)_S 46 _t (to)_S 46 _t (K=15,)_S 46 _t (using)_S 46 _t (the)_S 47 _t (results)_S 46 _t (of)_S 46 _t (the)_S 46 _t (previous)_S 46 _t (solution)_S 46 _t (as)_S 47 _t (the)_S 46 _t (starting)_S 46 _t (estimate)_S 46 _t (with)_S 46 _t (K)_S 46 _t (increased)_S 1200 5250 _m (by)_S 57 _t (1.)_S 116 _t (This)_S 57 _t (requires)_S 58 _t (many)_S 57 _t (more)_S 58 _t (iterations)_S 58 _t (overall)_S 57 _t (for)_S 58 _t (this)_S 58 _t (problem,)_S 58 _t (and)_S 57 _t (this)_S 58 _t (type)_S 58 _t (of)_S 57 _t (continuation)_S 58 _t (does)_S 58 _t (so)_S 1200 5050 _m (in)_S 61 _t (general,)_S 61 _t (compared)_S 61 _t (to)_S 61 _t (being)_S 61 _t (able)_S 61 _t (to)_S 61 _t (solve)_S 61 _t (in)_S 61 _t (one)_S 61 _t (step.)_S 61 _t 1620 4650 _m (If)_S 59 _t (no)_S 59 _t (solution)_S 59 _t (has)_S 59 _t (been)_S 59 _t (found)_S 59 _t (yet,)_S 59 _t (it)_S 59 _t (is)_S 59 _t (unlikely)_S 59 _t (that)_S 59 _t (NNES)_S 59 _t (will)_S 59 _t (be)_S 59 _t (able)_S 59 _t (to)_S 59 _t (find)_S 59 _t (it.)_S 118 _t (There)_S 59 _t (are)_S 59 _t (other)_S 1200 4450 _m (methods)_S 72 _t (available)_S 72 _t (such)_S 72 _t (as)_S 72 _t (true)_S 72 _t (continuation)_S 72 _t (methods.)_S 144 _t (Several)_S 72 _t (are)_S 72 _t (available)_S 72 _t (through)_S 72 _t (NetLib.)_S 144 _t (General)_S 1200 4250 _m (references)_S 49 _t (are)_S 50 _t (the)_S 49 _t (books)_S 50 _t (by)_S 50 _t (Garcia)_S 49 _t (and)_S 50 _t (Zangwill)_S 49 _t (\(1981\),)_S 50 _t (Morgan)_S 50 _t (\(1987\))_S 49 _t (and)_S 50 _t (Allgower)_S 49 _t (and)_S 50 _t (Georg)_S 50 _t (\(1990\).)_S 1200 4050 _m (The)_S 49 _t (last)_S 50 _t (two)_S 50 _t (have)_S 49 _t (FORTRAN)_S 50 _t (code)_S 49 _t (included.)_S 100 _t (Also,)_S 49 _t (Shacham)_S 50 _t (\(1986\))_S 49 _t (lists)_S 50 _t (the)_S 50 _t (FORTRAN)_S 50 _t (source)_S 49 _t (code)_S 50 _t (for)_S 1200 3850 _m (his)_S 61 _t (simple)_S 61 _t (continuation)_S 61 _t (method.)_S 1620 3650 _m (Another)_S 70 _t (developing)_S 69 _t (area)_S 70 _t (is)_S 69 _t (interval)_S 70 _t (methods)_S 69 _t (which)_S 70 _t (use)_S 70 _t (a)_S 69 _t (different)_S 70 _t (approach)_S 69 _t (than)_S 70 _t (Newton-)_S 69 _t (based)_S 1200 3450 _m (methods;)_S 73 _t (see)_S 72 _t (Neumaier)_S 72 _t (\(1990\))_S 72 _t (for)_S 72 _t (a)_S 72 _t (description)_S 72 _t (of)_S 73 _t (these)_S 72 _t (methods.)_S 144 _t (These)_S 73 _t (methods)_S 72 _t (do)_S 72 _t (not)_S 72 _t (require)_S 72 _t (the)_S 1200 3250 _m (closeness)_S 74 _t (condition)_S 74 _t (which)_S 73 _t (defeats)_S 74 _t (Newton's)_S 74 _t (method;)_S 74 _t (all)_S 74 _t (that)_S 74 _t (is)_S 74 _t (required)_S 74 _t (is)_S 74 _t (an)_S 74 _t (initial)_S 74 _t (interval)_S 74 _t (for)_S 74 _t (each)_S 1200 3050 _m (component)_S 61 _t (in)_S 61 _t (which)_S 60 _t (the)_S 61 _t (solution)_S 61 _t (lies.)_S 121 _t (Kearfott)_S 61 _t (\(1990\))_S 60 _t (has)_S 61 _t (made)_S 60 _t (an)_S 61 _t (interval)_S 61 _t (bisection)_S 60 _t (method,)_S 61 _t (INTBIS,)_S 1200 2850 _m (available)_S 61 _t (through)_S 61 _t (NetLib.)_S 1620 2650 _m (A)_S 58 _t (third)_S 58 _t (alternative)_S 59 _t (are)_S 58 _t (the)_S 58 _t (ABS)_S 58 _t (\(Abaffy,)_S 58 _t (Broyden)_S 58 _t (and)_S 58 _t (Spedicato\))_S 59 _t (projection)_S 58 _t (methods)_S 58 _t (as)_S 58 _t (advocated)_S 1200 2450 _m (by)_S 61 _t (Abaffy)_S 61 _t (and)_S 61 _t (Spedicato)_S 61 _t (\(1989\).)_S 1620 2250 _m (At)_S 43 _t (the)_S 44 _t (time)_S 43 _t (of)_S 44 _t (writing,)_S 43 _t (the)_S 44 _t (solvers)_S 43 _t (available)_S 44 _t (from)_S 43 _t (MINPACK,)_S 44 _t (NAG)_S 44 _t (and)_S 43 _t (IMSL)_S 44 _t (are)_S 43 _t (based)_S 44 _t (on)_S 43 _t (the)_S 44 _t (same)_S 1200 2050 _m (principles)_S 61 _t (as)_S 61 _t (NNES)_S 61 _t (so)_S 61 _t (are)_S 61 _t (unlikely)_S 61 _t (to)_S 61 _t (succeed)_S 61 _t (where)_S 61 _t (NNES)_S 61 _t (fails.)_S 4886 1250 _m (-)_S 61 _t (15)_S 61 _t (-)_S _ep _bp /Times-RomanR 550 _ff 0 13200 10200 _ornt /_r { sflg {/_t {0 rmoveto}bdef /ron false def} { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse }bdef 1200 11850 _m /Times-BoldR 550 _ff (3.)_S 61 _t (General)_S 61 _t (Description)_S 61 _t (of)_S 61 _t (NNES)_S /Times-RomanR 550 _ff 1620 11450 _m (Recall,)_S 61 _t (NNES)_S 61 _t (is)_S 61 _t (intended)_S 61 _t (to)_S 61 _t (solve)_S 61 _t (problems)_S 61 _t (of)_S 61 _t (the)_S 61 _t (form:)_S 1200 9954 _m (given)_S 54 _t (an)_S 53 _t (initial)_S 53 _t (estimate,)_S 53 _t /Times-BoldR 550 _ff (x)_S /Times-RomanR 330 _ff 3170 9913 _m (0)_S 3225 9913 _m /Times-RomanR 550 _ff 3225 9954 _m (.)_S 107 _t (It)_S 54 _t (encompasses)_S 53 _t (four)_S 53 _t (general)_S 54 _t (approaches)_S 53 _t (to)_S 53 _t (solving)_S 54 _t (these)_S 53 _t (systems:)_S 53 _t (Newton's)_S gsave 0 0 translate 4 4 scale _s 3 _w 65 1899 325 2760 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale 1192 2809 16 _ieq F01F 1456 2809 16 _ieq FE38 1120 2808 88 _ieq 7FFFFFBFFFFFFFFFFFE00F 1456 2808 24 _ieq F0307F 1080 2807 128 _ieq E000000FFE7FFFFF9FFFFFFFFFFFC007 1296 2807 32 _ieq C000001F 1424 2807 56 _ieq F800003FF8607F 1080 2806 128 _ieq C000000FFCFFFFFFC7FFFFFFFFFF8303 1296 2806 32 _ieq 8000001F 1424 2806 56 _ieq F800000FFC487F 1080 2805 128 _ieq F800000FF8FFFFFFE3FFFFFFFFFF8783 1296 2805 32 _ieq F000001F 1432 2805 40 _ieq 8C0007FC18 1080 2804 128 _ieq F803F81FF1FFFFFFF1FFFFFFFFFE0781 1296 2804 32 _ieq F007F03F 1432 2804 40 _ieq 8C7863FCB8 1080 2803 128 _ieq F807FE1FE3FFFFFFF8FFFFFFFFFC0781 1296 2803 32 _ieq F00FFC3F 1432 2803 40 _ieq 8C7C33F878 1080 2802 128 _ieq F807FE1FC7FFFFFFFC7FFFFFFFFC0780 1296 2802 32 _ieq F00FFC3F 1432 2802 40 _ieq 8C7E39F870 1080 2801 128 _ieq F80FFF1F8FFFFFFFFC3FFFFFFFFC0780 1296 2801 32 _ieq F01FFE3F 1432 2801 40 _ieq 8C7E39F8F1 1080 2800 136 _ieq F00FFF3F9FFFFFFFFE3FFFFFFFF807807F 1296 2800 32 _ieq E01FFE7F 1432 2800 40 _ieq 8C7E39F8E1 1080 2799 136 _ieq F00FFF3F1FFFFFFFFE1FFFFFFFF80F807F 1296 2799 32 _ieq E01FFE7F 1432 2799 48 _ieq 8C7E39F1E17F 1080 2798 136 _ieq F01FE33E1FFF07F1FE0FFFFFFFF80FC03F 1296 2798 184 _ieq E03FC67FFFFFF83F8FFFFFFFE01FFFFFFF8C7E39F1E13F 1080 2797 136 _ieq F01FC3FE1FF007E0FF0FFFFFFFF80FC03F 1296 2797 184 _ieq 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(where)_S 1200 3946 _m (Newton)_S 82 _t (steps)_S 81 _t (may)_S 82 _t (be)_S 81 _t (taken)_S 82 _t (to)_S 81 _t (ultimately)_S 81 _t (achieve)_S 82 _t (quadratic)_S 81 _t (convergence)_S 82 _t (while)_S 81 _t (taking)_S 82 _t (precautions)_S 81 _t (to)_S 1200 3746 _m (prevent)_S 61 _t (divergence.)_S 1620 3346 _m (The)_S 59 _t (Jacobian)_S 59 _t (matrix)_S 59 _t (can)_S 59 _t (be)_S 59 _t (evaluated)_S 60 _t (explicitly)_S 59 _t (in)_S 59 _t (this)_S 59 _t (and)_S 59 _t (all)_S 59 _t (other)_S 59 _t (methods)_S 59 _t (in)_S 59 _t (one)_S 60 _t (of)_S 59 _t (four)_S 59 _t (ways:)_S 1200 3146 _m (analytically)_S 57 _t (using)_S 58 _t (a)_S 57 _t (user-supplied)_S 58 _t (subroutine)_S 57 _t (\(the)_S 57 _t (examples)_S 58 _t (use)_S 57 _t (JACOB\);)_S 57 _t (forward)_S 58 _t (differences;)_S 57 _t (backward)_S 1200 2946 _m (differences)_S 46 _t (and)_S 46 _t (central)_S 46 _t (differences.)_S 92 _t (The)_S 46 _t (evaluation)_S 45 _t (method)_S 46 _t (is)_S 46 _t (controlled)_S 46 _t 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2016 160 _ieq FE00000FF0707FFFFFFFFFFFFFFFE03C07FC1C1F 880 2015 8 _ieq BF 1056 2015 80 _ieq FEFFFFFFFFFFFFFFFF07 1512 2015 160 _ieq E000001FE0707FFFFFFFFFFFFFFFF0000FF81C1F 880 2014 8 _ieq 3F 976 2014 200 _ieq E0000FFFFFFFFFFFFFFFFE7FFFFFFFFFFFFFFF07FFFC00007F 1512 2014 160 _ieq E00000FFE0707FFFFFFFFFFFFFFFF8001FF81C1F 872 2013 16 _ieq FE7F 976 2013 200 _ieq C00003FFFFFFFFFFFFFFFF1FFFFFFFFFFFFFFF07FFF800001F 1544 2013 128 _ieq E0707FFFFFFFFFFFFFFFFE003FF81C1F 872 2012 16 _ieq FC7F 976 2012 200 _ieq F80000FFFFFFFFFFFFFFFF8FFFFFFFFFFFFFFF07FFFF00000F 1544 2012 128 _ieq E0707FFFFFFFFFFFFFFFFF80FFF81C1F 872 2011 8 _ieq F8 976 2011 200 _ieq F807807FFFFFFFFFFFFFFFC7FFFFFFFFFFFFFE0FFFFF00F80F 1544 2011 24 _ieq E0707F 1648 2011 24 _ieq F81C1F 872 2010 8 _ieq F3 976 2010 200 _ieq F807C03FFFFFFFFFFFFFFFE3FFFFFFFFFFFFFE0FFFFF00FC0F 1544 2010 24 _ieq E0707F 1648 2010 24 _ieq F81C1F 872 2009 8 _ieq E3 976 2009 200 _ieq F807C03FFFFFFFFFFFFFFFF1FFFFFFFFFFFFFE0FFFFF00FC07 1544 2009 24 _ieq E0707F 1648 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1792 1949 16 _ieq E08F 592 1948 200 _ieq FC00001FFF87FFFFFFF07FFFFFFFFFFFFFFFFF800003FFF87F 1232 1948 16 _ieq 803F 1328 1948 104 _ieq 8FF8FFE0FE03F803FE1FFFE00F 1544 1948 16 _ieq F84F 1648 1948 48 _ieq FE13FF0003E0 1792 1948 16 _ieq E13F 632 1947 48 _ieq 07FFFC7FF07F 776 1947 16 _ieq F07F 1232 1947 16 _ieq C03F 1328 1947 104 _ieq 8FFDFFFFFE0FFC07FFFFFFF01F 1544 1947 16 _ieq F80F 1648 1947 48 _ieq FE03FF0003E0 1792 1947 16 _ieq E03F 632 1946 48 _ieq 0807FC7FF07F 776 1946 24 _ieq F0807F 1232 1946 16 _ieq E03F 1328 1946 104 _ieq DFFFFFFFFF1FFE0FFFFFFFF83F 1544 1946 16 _ieq F007 1648 1946 48 _ieq FC01FFF87FE0 1792 1946 16 _ieq C01F 632 1945 48 _ieq 0C0FFC7FF07F 776 1945 16 _ieq F0C0 1232 1945 16 _ieq FC3F 1544 1945 16 _ieq F087 1648 1945 48 _ieq FC21FFF87FE0 1792 1945 16 _ieq C21F 624 1944 56 _ieq FE0C3FFC7FF07F 776 1944 16 _ieq E0C3 1232 1944 16 _ieq FC3F 1544 1944 16 _ieq F087 1648 1944 48 _ieq FC21FFF87FE0 1792 1944 16 _ieq C21F 624 1943 56 _ieq FE08FFFC7FF07F 776 1943 16 _ieq E08F 992 1943 24 _ieq F80003 1232 1943 16 _ieq F87F 1544 1943 24 _ieq E0837F 1648 1943 48 _ieq F820DFF87FE0 1792 1943 16 _ieq 820D 624 1942 56 _ieq FE13FF8003F07F 776 1942 16 _ieq E13F 992 1942 24 _ieq F80003 1232 1942 8 _ieq F0 1544 1942 24 _ieq E0827F 1648 1942 48 _ieq F8209FF87FE0 1792 1942 16 _ieq 8209 624 1941 56 _ieq FE03FF8003F07F 776 1941 16 _ieq E03F 992 1941 24 _ieq F8E0E3 1232 1941 8 _ieq 83 1544 1941 16 _ieq E1C0 1648 1941 48 _ieq F8703FFFFFC0 1792 1941 16 _ieq 8703 624 1940 56 _ieq FC01FFFC7FF07F 776 1940 16 _ieq C01F 992 1940 24 _ieq F1C1E7 1232 1940 8 _ieq 8F 1544 1940 16 _ieq C1C0 1648 1940 56 _ieq F0703FFFFE000F 1792 1940 16 _ieq 0703 624 1939 56 _ieq FC21FFFC7FF07F 776 1939 16 _ieq C21F 992 1939 24 _ieq F3C1E7 1544 1939 16 _ieq C1C1 1648 1939 56 _ieq F0707FFFFE000F 1792 1939 16 _ieq 0707 624 1938 56 _ieq FC21FFFC7FF07F 776 1938 16 _ieq C21F 992 1938 24 _ieq F7C1E7 1552 1938 8 _ieq E3 1656 1938 8 _ieq F8 1800 1938 8 _ieq 8F 624 1937 56 _ieq F820DFFC7FF07F 776 1937 16 _ieq 820D 1000 1937 8 _ieq C1 624 1936 56 _ieq F8209FFC7FF07F 776 1936 16 _ieq 8209 1000 1936 8 _ieq 83 624 1935 56 _ieq F8703FFFFFE07F 776 1935 16 _ieq 8703 1000 1935 48 _ieq 83FFFE00003F 624 1934 56 _ieq F0703FFFFF0007 776 1934 16 _ieq 0703 1000 1934 48 _ieq 83FFFC00000F 624 1933 56 _ieq F0707FFFFF0007 776 1933 16 _ieq 0707 1000 1933 48 _ieq 83FFFF800007 632 1932 8 _ieq F8 784 1932 8 _ieq 8F 1000 1932 48 _ieq 07FFFF807C07 1000 1931 48 _ieq 07FFFF807E07 1000 1930 48 _ieq 07FFFF807E03 1000 1929 48 _ieq 07FFFF807E03 992 1928 56 _ieq FE0FFFFF00FE03 992 1927 56 _ieq FE0FFFFF00FE03 960 1926 128 _ieq E0CFFFFFFE1FFFFF00FE03FFFFFF067F 960 1925 128 _ieq C00FFFFFFE1FFFFF01FC03FFFFFE007F 960 1924 128 _ieq 800FFFFFF003FFFE01FC03FFFFFC007F 1672 1924 8 _ieq FD 1760 1924 8 _ieq DF 1888 1924 56 _ieq FBFFFFFFFFFFF7 960 1923 128 _ieq 0F0FFFFFF007FFFE01F007FFFFF8787F 1632 1923 48 _ieq F8000003FFF9 1760 1923 8 _ieq CF 1848 1923 96 _ieq F0000007FFF3FFFFFFFFFFF3 960 1922 128 _ieq 0F0FFFFFFFFFFFFE03E00FFFFFF8787F 1632 1922 48 _ieq F0000003FFF3 1760 1922 8 _ieq E3 1848 1922 96 _ieq E0000007FFE7FFFFFFFFFFF8 952 1921 136 _ieq FE0F8FFFFFFFFFFFFE00003FFFFFF07C7F 1632 1921 48 _ieq FE00E003FFE3 1760 1921 8 _ieq F1 1848 1921 104 _ieq FC01C007FFC7FFFFFFFFFFFC7F 952 1920 136 _ieq FE078FFFFFFFFFFFFC00007FFFFFF03C7F 1632 1920 48 _ieq FE00FE07FFC7 1760 1920 8 _ieq F8 1848 1920 104 _ieq FC01FC0FFF8FFFFFFFFFFFFE3F 952 1919 136 _ieq FE078FFFFFFFFFFFFC0001FFFFFFF03C7F 1632 1919 48 _ieq FE01FF87FF9F 1760 1919 192 _ieq FC7FFFFFFFFFFFFFFFFFFFFC03FF0FFF3FFFFFFFFFFFFF1F 952 1918 128 _ieq FE03FFFFFFFFFFFFFC03FFFFFFFFF01F 1632 1918 48 _ieq FE01FF87FF1F 1760 1918 192 _ieq FE3FFFFFFFFFFFFFFFFFFFFC03FF0FFE3FFFFFFFFFFFFF8F 960 1917 120 _ieq 01FFFFFFFFFFFFFC07FFFFFFFFF80F 1632 1917 48 _ieq FE03FFC7FE3F 1760 1917 192 _ieq FE1FFFFFFFFFFFFFFFFFFFFC07FF8FFC7FFFFFFFFFFFFF87 960 1916 120 _ieq 80FFFFFFFFFFFFF807FFFFFFFFFC07 1632 1916 48 _ieq FC03FFCFFE7F 1768 1916 184 _ieq 1FFFFFFFFFFFFFFFFFFFF807FF9FFCFFFFFFFFFFFFFFC7 960 1915 120 _ieq 80FFFFFFFFFFFFF807FFFFFFFFFC07 1632 1915 48 _ieq FC03FFCFFC7F 1768 1915 184 _ieq 0FFFFFFFFFFFFFFFFFFFF807FF9FF8FFFFFFFFFFFFFFC3 960 1914 120 _ieq C07FFFFFFFFFFFF80FFFFFFFFFFE03 1528 1914 16 _ieq C3E1 1632 1914 320 _ieq FC07F8CFF87FFFE0FE3FFFFFFFFFFFFFFF07FFFFFFFFFFFFFFFFFFF80FF19FF0FFF83F8FFFFFFFC1 960 1913 120 _ieq C07FFFFFFFFFFFF80FFFFFFFFFFE03 1520 1913 24 _ieq FE03C0 1632 1913 320 _ieq FC07F0FFF87FFE00FC1FFFFFFFFFFFFFFF87FFFFFFFFFFFFFFFFFFF80FE1FFF0FF803F07FFFFFFE1 952 1912 128 _ieq F9E03FFFFFFFFFFFF01FFFFFFFFFCF01 1520 1912 32 _ieq FE03C07F 1632 1912 320 _ieq F807F1FFF07FFE00701FFFFFFFFFFFFFFF83FFFFFFFFFFFFFFFFFFF00FE3FFE0FF801C07FFFFFFE0 952 1911 144 _ieq F9F03FF8FFFFFFFFF01FFFFFE3FFCF81FFC7 1520 1911 432 _ieq FE01C07FFFFFFFFFF00003FFFFFFF80FE1FFF0FFFF00601FFFFFFFFFFFFFFF83FFFFFFFFFFFFFFFFFFF01FC3FFE1FFC01807FFFFFFE0 952 1910 144 _ieq F9F83F80FFFFFFFFF01FFFFE03FFCFC1FC07 1528 1910 432 _ieq 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E3 1712 1877 8 _ieq F1 1920 1877 16 _ieq FE3F _s grestore 8686 7834 _m /Times-BoldR 550 _ff (\(8\))_S /Times-RomanR 550 _ff gsave 0 0 translate 4 4 scale _s 155 1899 325 1630 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale 1152 1775 24 _ieq 80003F 1152 1774 24 _ieq 80003F 1152 1773 24 _ieq 8E0E3F 1152 1772 24 _ieq 1C1E7F 1152 1771 24 _ieq 3C1E7F 1152 1770 24 _ieq 7C1E7F 1152 1769 16 _ieq FC1F 1152 1768 16 _ieq F83F 1040 1767 24 _ieq 80001F 1152 1767 40 _ieq F83FFC0000 1040 1766 24 _ieq 000007 1152 1766 48 _ieq F83FF800003F 1040 1765 24 _ieq E00003 1152 1765 48 _ieq F83FFF00001F 1040 1764 24 _ieq E01F01 1152 1764 48 _ieq F07FFF00F80F 1040 1763 24 _ieq E01F81 1152 1763 48 _ieq F07FFF00FC0F 1040 1762 24 _ieq E01F80 1152 1762 48 _ieq F07FFF00FC07 1600 1762 24 _ieq 00003F 1704 1762 24 _ieq FC0007 1040 1761 24 _ieq E01F80 1152 1761 48 _ieq F07FFF00FC07 1592 1761 32 _ieq FE00000F 1704 1761 24 _ieq FC000F 1040 1760 24 _ieq C03F80 1152 1760 48 _ieq E0FFFE01FC07 1600 1760 24 _ieq C00007 1712 1760 16 _ieq 803F 1040 1759 24 _ieq C03F80 1152 1759 48 _ieq E0FFFE01FC07 1600 1759 24 _ieq C03E03 1712 1759 16 _ieq 807F 1040 1758 160 _ieq C03F80FFFFF873FFFFFE1CFFFFFFE1FFFE01FC07 1600 1758 24 _ieq C03F03 1712 1758 16 _ieq 807F 1040 1757 160 _ieq C07F00FFFFF003FFFFFC00FFFFFFE1FFFE03F807 1600 1757 24 _ieq C03F01 1712 1757 8 _ieq 80 1040 1756 160 _ieq 807F00FFFFE003FFFFF800FFFFFF003FFC03F807 1600 1756 24 _ieq C03F01 1712 1756 8 _ieq 80 1040 1755 160 _ieq 807C01FFFFC383FFFFF0E0FFFFFF007FFC03E00F 1600 1755 24 _ieq 807F01 1712 1755 8 _ieq 01 1040 1754 160 _ieq 80F803FFFFC3C3FFFFF0F0FFFFFFFFFFFC07C01F 1600 1754 24 _ieq 807F01 1712 1754 8 _ieq 01 1040 1753 160 _ieq 80000FFFFF83E3FFFFE0F8FFFFFFFFFFFC00007F 1600 1753 24 _ieq 807F01 1712 1753 8 _ieq 01 1040 1752 152 _ieq 00001FFFFF81E3FFFFE078FFFFFFFFFFF80000 1600 1752 24 _ieq 80FE01 1704 1752 16 _ieq FE01 1040 1751 152 _ieq 00007FFFFF81E3FFFFE078FFFFFFFFFFF80003 1600 1751 24 _ieq 00FE01 1704 1751 16 _ieq FE03 1040 1750 144 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160 _ieq FE0827FFFF8209FFFFE0827FFFFFFFFFFFF0413F 1432 1726 16 _ieq FC3F 1616 1726 24 _ieq F81C1F 720 1725 32 _ieq F807E03F 864 1725 32 _ieq F807E03F 1056 1725 160 _ieq FE1C0FFFFF8703FFFFE1C0FFFFFFFFFFFFF0E07F 1432 1725 16 _ieq F83F 1616 1725 24 _ieq F81C1F 720 1724 32 _ieq F00FE03F 864 1724 32 _ieq F00FE03F 1056 1724 160 _ieq FC1C0FFFFF0703FFFFC1C0FFFFFFFFFFFFE0E07F 1432 1724 16 _ieq F83F 1616 1724 24 _ieq F81C1F 720 1723 32 _ieq F00FE03F 864 1723 32 _ieq F00FE03F 1056 1723 152 _ieq FC1C1FFFFF0707FFFFC1C1FFFFFFFFFFFFE0E0 1432 1723 16 _ieq F87F 1616 1723 24 _ieq F81C1F 720 1722 32 _ieq F00FE03F 864 1722 32 _ieq F00FE03F 1064 1722 144 _ieq FE3FFFFFFF8FFFFFFFE3FFFFFFFFFFFFFFF1 1400 1722 112 _ieq FCFFDFE1F87E1FFFC3FF838FFF0F 1616 1722 24 _ieq F81C1F 720 1721 32 _ieq F01FC03F 864 1721 32 _ieq F01FC03F 1400 1721 112 _ieq E07F8FC1F07C0FFF00F80307FC03 1616 1721 24 _ieq FC1C3F 720 1720 32 _ieq E01FC03F 864 1720 32 _ieq E01FC03F 1400 1720 112 _ieq 807F8FC0F0600FFC00780407F001 1616 1720 24 _ieq 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112 _ieq 047FFFFFFFFFFFFF823FFFFFE08F 1152 1652 112 _ieq 09FFFFFFFFFFFFFF84FFFFFFE13F 1152 1651 112 _ieq 01FFFFFFFFFFFFFF80FFFFFFE03F 1144 1650 120 _ieq FE00FFFFFFFFFFFFFF007FFFFFC01F 1144 1649 120 _ieq FE10FFFFFFFFFFFFFF087FFFFFC21F 1144 1648 120 _ieq FE10FFFFFFFFFFFFFF087FFFFFC21F 1144 1647 120 _ieq FC106FFFFFFFFFFFFE0837FFFF820D 1144 1646 120 _ieq FC104FFFFFFFFFFFFE0827FFFF8209 1144 1645 120 _ieq FC381FFFFFFFFFFFFE1C0FFFFF8703 1144 1644 120 _ieq F8381FFFFFFFFFFFFC1C0FFFFF0703 1144 1643 120 _ieq F8383FFFFFFFFFFFFC1C1FFFFF0707 1152 1642 112 _ieq FC7FFFFFFFFFFFFFFE3FFFFFFF8F _s grestore 8686 6823 _m /Times-BoldR 550 _ff (\(9\))_S /Times-RomanR 550 _ff 1200 5810 _m (affected)_S 61 _t (by)_S 61 _t (the)_S 61 _t (choice)_S 61 _t (of)_S 61 _t /Symbol 550 _ff (w)_S /Times-RomanR 550 _ff (.)_S 1620 5410 _m (The)_S 61 _t (only)_S 62 _t (information)_S 61 _t (used)_S 61 _t (in)_S 62 _t (the)_S 61 _t (updates)_S 61 _t (is)_S 61 _t (the)_S 62 _t (current)_S 61 _t (step,)_S 61 _t /Times-BoldR 550 _ff (s)_S /Times-RomanR 330 _ff 6312 5369 _m (k)_S 6367 5369 _m /Times-RomanR 550 _ff 6367 5410 _m (,)_S 62 _t (and)_S 61 _t (the)_S 61 _t (difference)_S 61 _t (of)_S 62 _t (the)_S 61 _t (function)_S 1200 5210 _m (vectors,)_S 53 _t /Times-BoldR 550 _ff (F)_S /Times-RomanR 550 _ff (\()_S /Times-BoldR 550 _ff (x)_S /Times-RomanR 330 _ff 2093 5169 _m (k+1)_S 2265 5169 _m /Times-RomanR 550 _ff 2265 5210 _m (\))_S 54 _t (-)_S 53 _t /Times-BoldR 550 _ff (F)_S /Times-RomanR 550 _ff (\()_S /Times-BoldR 550 _ff (x)_S /Times-RomanR 330 _ff 2759 5169 _m (k)_S 2814 5169 _m /Times-RomanR 550 _ff 2814 5210 _m (\).)_S 107 _t (In)_S 53 _t (NNES,)_S 54 _t (a)_S 53 _t (scale-invariant)_S 54 _t (version)_S 53 _t (of)_S 54 _t (the)_S 53 _t (above)_S 53 _t (methods)_S 54 _t (is)_S 53 _t (implemented.)_S 107 _t (Also,)_S 1200 5010 _m (only)_S 74 _t (the)_S 73 _t (rows)_S 74 _t (which)_S 74 _t (make)_S 73 _t (a)_S 74 _t (significant)_S 74 _t (change)_S 73 _t (to)_S 74 _t (the)_S 74 _t (current)_S 74 _t /Times-BoldR 550 _ff (B)_S /Times-RomanR 550 _ff 73 _t (matrix)_S 74 _t (are)_S 74 _t (added.)_S 147 _t (If)_S 74 _t (the)_S 73 _t (problem)_S 74 _t (is)_S 1200 4810 _m (suspected)_S 69 _t (to)_S 70 _t (be)_S 70 _t (sensitive)_S 69 _t (to)_S 70 _t (the)_S 70 _t (initial)_S 70 _t (steps,)_S 69 _t (the)_S 70 _t (option)_S 69 _t (is)_S 70 _t (available)_S 70 _t (to)_S 70 _t (delay)_S 69 _t (the)_S 70 _t (start)_S 70 _t (of)_S 70 _t (quasi-Newton)_S 1200 4610 _m (updates)_S 43 _t (by)_S 44 _t (setting)_S 43 _t (the)_S 44 _t (variable)_S 43 _t (NIEJEV,)_S 44 _t (the)_S 43 _t (number)_S 44 _t (of)_S 43 _t (initial)_S 43 _t (steps)_S 44 _t (in)_S 43 _t (which)_S 43 _t (the)_S 44 _t (Jacobian)_S 43 _t (will)_S 44 _t (be)_S 43 _t (evaluated)_S 1200 4410 _m (explicitly.)_S 1620 4010 _m (As)_S 86 _t (presented)_S 87 _t (above,)_S 87 _t (the)_S 87 _t (updated)_S 86 _t (approximate)_S 87 _t (Jacobian)_S 86 _t (then)_S 87 _t (has)_S 87 _t (to)_S 87 _t (be)_S 86 _t (factored)_S 87 _t (\(using)_S 87 _t (the)_S 87 _t (QR)_S 1200 3810 _m (decomposition)_S 84 _t (in)_S 84 _t (NNES\))_S 84 _t (before)_S 85 _t (the)_S 84 _t (linear)_S 84 _t (system,)_S 84 _t (equation)_S 84 _t (\(4\),)_S 84 _t (with)_S 84 _t /Times-BoldR 550 _ff (B)_S /Times-RomanR 550 _ff 85 _t (replacing)_S 84 _t /Times-BoldR 550 _ff (J)_S /Times-RomanR 550 _ff (,)_S 84 _t (can)_S 84 _t (be)_S 84 _t (solved.)_S 1200 3610 _m (Instead)_S 40 _t (of)_S 41 _t (updating)_S 40 _t (the)_S 40 _t (Jacobian)_S 41 _t (and)_S 40 _t (factoring,)_S 40 _t (the)_S 41 _t (default)_S 40 _t (quasi-Newton)_S 40 _t (update)_S 41 _t (method,)_S 40 _t (set)_S 40 _t (by)_S 41 _t (QNUPDM,)_S 1200 3410 _m (is)_S 69 _t (to)_S 70 _t (update)_S 70 _t (the)_S 70 _t (QR)_S 70 _t (factors)_S 70 _t (directly.)_S 140 _t (This)_S 70 _t (is)_S 69 _t (a)_S 70 _t (time-saving)_S 70 _t (step)_S 70 _t (and)_S 70 _t (usually)_S 70 _t (leads)_S 70 _t (to)_S 70 _t (exactly)_S 70 _t (the)_S 70 _t (same)_S 1200 3210 _m (solution)_S 53 _t (as)_S 52 _t (formulating)_S 52 _t (the)_S 53 _t (approximate)_S 52 _t (Jacobian)_S 52 _t (then)_S 52 _t (factoring.)_S 105 _t (Only)_S 52 _t (in)_S 52 _t (very)_S 53 _t (sensitive)_S 52 _t (problems,)_S 52 _t (where)_S 1200 3010 _m (numerical)_S 47 _t (accuracy)_S 46 _t (in)_S 47 _t (the)_S 46 _t (last)_S 46 _t (few)_S 47 _t (digits)_S 46 _t (is)_S 47 _t (important,)_S 46 _t (will)_S 46 _t (this)_S 47 _t (choice)_S 46 _t (make)_S 46 _t (a)_S 47 _t (difference.)_S 93 _t (The)_S 46 _t (other)_S 46 _t (utility)_S 1200 2810 _m (of)_S 54 _t (using)_S 54 _t (the)_S 54 _t (unfactored)_S 55 _t (update)_S 54 _t (is)_S 54 _t (that)_S 54 _t (the)_S 54 _t (user)_S 54 _t (may)_S 54 _t (want)_S 54 _t (to)_S 54 _t (see)_S 54 _t (what)_S 54 _t (is)_S 54 _t (happening)_S 54 _t (to)_S 54 _t /Times-BoldR 550 _ff (B)_S /Times-RomanR 550 _ff 54 _t (in)_S 54 _t (case)_S 54 _t (of)_S 54 _t (failure,)_S 1200 2610 _m (e.g.,)_S 57 _t (are)_S 58 _t (some)_S 57 _t (entries)_S 57 _t (becoming)_S 58 _t (extremely)_S 57 _t (large)_S 58 _t (or)_S 57 _t (are)_S 57 _t (sparsity)_S 58 _t (patterns)_S 57 _t (within)_S 57 _t (the)_S 58 _t (actual)_S 57 _t (Jacobian)_S 57 _t (being)_S 1200 2410 _m (lost.)_S 4886 1250 _m (-)_S 61 _t (17)_S 61 _t (-)_S _ep _bp /Times-RomanR 550 _ff 0 13200 10200 _ornt /_r { sflg {/_t {0 rmoveto}bdef /ron false def} { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse }bdef 1620 11850 _m (The)_S 47 _t (other)_S 46 _t (options)_S 47 _t (for)_S 47 _t (Newton's)_S 47 _t (method)_S 47 _t (are)_S 47 _t (the)_S 47 _t (stopping)_S 47 _t (criteria.)_S 93 _t (These)_S 47 _t (are)_S 47 _t (based)_S 47 _t (on)_S 47 _t (either)_S 47 _t (step)_S 47 _t (size)_S 1200 11650 _m (or)_S 53 _t (function)_S 53 _t (value;)_S 52 _t (the)_S 53 _t (choice)_S 52 _t (is)_S 53 _t (determined)_S 53 _t (by)_S 52 _t (setting)_S 53 _t (STOPCR.)_S 105 _t (There)_S 52 _t (are,)_S 53 _t (in)_S 53 _t (fact,)_S 52 _t (two)_S 53 _t (step)_S 52 _t (size)_S 53 _t (criteria.)_S 1200 11450 _m (The)_S 63 _t (first)_S 62 _t (is)_S 63 _t (governed)_S 62 _t (by)_S 63 _t (the)_S 62 _t (constant)_S 63 _t (NSTTOL)_S 63 _t (and)_S 62 _t (the)_S 63 _t (second)_S 62 _t (by)_S 63 _t (STPTOL.)_S 125 _t (In)_S 62 _t (Newton's)_S 63 _t (method)_S 62 _t (they)_S 1200 11250 _m (measure)_S 52 _t (essentially)_S 51 _t (the)_S 51 _t (same)_S 52 _t (thing,)_S 51 _t (as)_S 52 _t (step)_S 51 _t (length)_S 52 _t (is)_S 51 _t (not)_S 51 _t (modified)_S 52 _t (by)_S 51 _t (a)_S 52 _t (line)_S 51 _t (search)_S 52 _t (or)_S 51 _t (trust)_S 51 _t (region,)_S 52 _t (so)_S 51 _t (only)_S 1200 11050 _m (the)_S 58 _t (first)_S 58 _t (will)_S 57 _t (be)_S 58 _t (shown.)_S 58 _t (The)_S 57 _t (difference)_S 58 _t (will)_S 58 _t (be)_S 57 _t (explained)_S 58 _t (in)_S 58 _t (\2473.2.)_S 115 _t (Occasionally,)_S 58 _t (very)_S 57 _t (small)_S 58 _t (steps)_S 58 _t (will)_S 57 _t (be)_S 1200 10850 _m (taken)_S 62 _t (as)_S 62 _t (the)_S 63 _t (iterations)_S 62 _t (pass)_S 63 _t (through)_S 62 _t (a)_S 63 _t /Times-ItalicR 550 _ff (n)_S /Times-RomanR 550 _ff (-dimensional)_S 62 _t (flat)_S 62 _t (spot;)_S 62 _t (because)_S 63 _t (NNES)_S 62 _t (converges)_S 63 _t (with)_S 62 _t (respect)_S 63 _t (to)_S 1200 10650 _m (step)_S 73 _t (size)_S 73 _t (does)_S 74 _t (not)_S 73 _t (necessarily)_S 74 _t (mean)_S 73 _t (that)_S 74 _t (a)_S 73 _t (solution)_S 73 _t (has)_S 74 _t (been)_S 73 _t (found.)_S 147 _t (On)_S 73 _t (the)_S 74 _t (other)_S 73 _t (hand,)_S 74 _t (the)_S 73 _t (step)_S 74 _t (size)_S 1200 10450 _m (criterion)_S 61 _t (can)_S 61 _t (save)_S 61 _t (needless)_S 61 _t (steps)_S 61 _t (refining)_S 61 _t (accuracy)_S 61 _t (to)_S 61 _t (greater)_S 61 _t (than)_S 61 _t (that)_S 61 _t (needed.)_S 1620 10050 _m (The)_S 57 _t (Newton)_S 57 _t (step)_S 56 _t (stopping)_S 57 _t (criterion)_S 57 _t (looks)_S 57 _t (at)_S 57 _t (the)_S 57 _t (scaled)_S 56 _t (max-norm)_S 57 _t (of)_S 57 _t (the)_S 57 _t (Newton)_S 57 _t (step)_S 57 _t (calculated)_S 56 _t (in)_S 1200 9850 _m (equation)_S 61 _t (\(4\).)_S 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61 _t (method)_S 60 _t (is)_S 61 _t (similar)_S 61 _t (to)_S 61 _t (Newton's)_S 61 _t (method)_S 60 _t (except)_S 61 _t (that)_S 61 _t (all)_S 61 _t (the)_S 61 _t (steps)_S 61 _t (are)_S 61 _t (forced)_S 1200 6290 _m (to)_S 78 _t (be)_S 77 _t (inside)_S 78 _t (a)_S 78 _t (feasible)_S 77 _t (region)_S 78 _t (as)_S 77 _t (shown)_S 78 _t (in)_S 78 _t (Figure)_S 78 _t (1)_S 77 _t (\(p2\).)_S 156 _t (The)_S 77 _t (options)_S 78 _t (available)_S 77 _t (are)_S 78 _t (the)_S 78 _t (same)_S 77 _t (as)_S 78 _t (for)_S 1200 6090 _m (Newton's)_S 66 _t (method,)_S 66 _t (except)_S 66 _t (that)_S 67 _t (lower)_S 66 _t (and/or)_S 66 _t (upper)_S 66 _t (bounds)_S 66 _t (must)_S 66 _t (be)_S 67 _t (set)_S 66 _t (using)_S 66 _t (the)_S 66 _t (vectors)_S 66 _t (BOUNDL)_S 66 _t (and)_S 1200 5890 _m (BOUNDU.)_S 92 _t (Though)_S 46 _t (it)_S 46 _t (is)_S 45 _t (not)_S 46 _t (particularly)_S 46 _t (elegant,)_S 46 _t (Morgan)_S 45 _t (\(1987\))_S 46 _t (showed)_S 46 _t (that)_S 46 _t (this)_S 46 _t (method)_S 46 _t (can)_S 46 _t (be)_S 45 _t (effective)_S 1200 5690 _m (for)_S 59 _t (constrained)_S 58 _t (problems.)_S 118 _t (In)_S 59 _t (simple)_S 58 _t (terms,)_S 59 _t (the)_S 59 _t (iterations)_S 58 _t (bounce)_S 59 _t (around)_S 58 _t (inside)_S 59 _t (a)_S 59 _t (user-defined)_S 58 _t (box)_S 59 _t (until,)_S 1200 5490 _m (hopefully,)_S 57 _t (a)_S 56 _t (point)_S 56 _t (is)_S 56 _t (found)_S 57 _t (at)_S 56 _t (which)_S 56 _t (the)_S 56 _t (iterations)_S 56 _t (begin)_S 56 _t (to)_S 56 _t (converge.)_S 113 _t (In)_S 56 _t (fact,)_S 56 _t (the)_S 57 _t (method)_S 56 _t (in)_S 56 _t (NNES)_S 56 _t (is)_S 56 _t (an)_S 1200 5290 _m (extension)_S 61 _t (of)_S 61 _t (Morgan's)_S 61 _t (method)_S 61 _t (which)_S 61 _t (has)_S 61 _t (only)_S 61 _t (lower)_S 61 _t (bound)_S 61 _t (of)_S 61 _t /Times-BoldR 550 _ff (0)_S /Times-RomanR 550 _ff (,)_S 61 _t (hence)_S 61 _t (the)_S 61 _t (name)_S 61 _t ("Absolute".)_S 1620 4890 _m (The)_S 72 _t (difficulty)_S 73 _t (with)_S 72 _t (Newton's)_S 73 _t (method)_S 72 _t (and)_S 73 _t (Absolute)_S 72 _t (Newton's)_S 73 _t (method)_S 72 _t (is)_S 73 _t (that)_S 72 _t (they)_S 73 _t (are)_S 72 _t (only)_S 73 _t (local)_S 1200 4690 _m (methods.)_S 110 _t (Convergence)_S 56 _t (proofs)_S 55 _t (for)_S 55 _t (Newton's)_S 55 _t (methods,)_S 56 _t (given)_S 55 _t (for)_S 55 _t (example)_S 55 _t (in)_S 56 _t (Dennis)_S 55 _t (and)_S 56 _t (Schnabel)_S 55 _t (\(1983\))_S 1200 4490 _m (and)_S 59 _t (Ortega)_S 59 _t (and)_S 59 _t (Rheinboldt)_S 59 _t (\(1970\),)_S 60 _t (describe)_S 59 _t (the)_S 59 _t (conditions)_S 59 _t (under)_S 59 _t (which)_S 59 _t (Newton's)_S 59 _t (method)_S 59 _t (is)_S 59 _t (guaranteed)_S 1200 4290 _m (to)_S 52 _t (converge.)_S 103 _t (However,)_S 52 _t (these)_S 52 _t (conditions)_S 52 _t (are)_S 51 _t (so)_S 52 _t (restrictive)_S 52 _t (that)_S 52 _t (they)_S 51 _t (are)_S 52 _t (of)_S 52 _t (little)_S 52 _t (use)_S 51 _t (in)_S 52 _t (practice.)_S 104 _t (Newton's)_S 1200 4090 _m (method)_S 67 _t (will)_S 67 _t (converge)_S 67 _t (in)_S 67 _t (cases)_S 67 _t (where)_S 67 _t (theses)_S 67 _t (conditions)_S 67 _t (are)_S 67 _t (not)_S 67 _t (met.)_S 134 _t (There)_S 67 _t (is)_S 67 _t (also)_S 67 _t (no)_S 68 _t (practical)_S 67 _t (way)_S 67 _t (of)_S 1200 3890 _m (checking)_S 61 _t (to)_S 61 _t (see)_S 61 _t (if)_S 61 _t (the)_S 61 _t (criteria)_S 61 _t (are)_S 61 _t (met)_S 61 _t /Times-ItalicR 550 _ff (a)_S 61 _t (priori)_S /Times-RomanR 550 _ff (.)_S 1620 3490 _m (Because)_S 51 _t (of)_S 51 _t (this)_S 52 _t (limited)_S 51 _t (range)_S 51 _t (of)_S 51 _t (convergence,)_S 51 _t (so-called)_S 51 _t (global)_S 51 _t (methods)_S 51 _t (have)_S 51 _t (been)_S 51 _t (developed)_S 51 _t (which)_S 1200 3290 _m (are)_S 50 _t (designed)_S 49 _t (to)_S 50 _t (converge)_S 50 _t (from)_S 49 _t (any)_S 50 _t (starting)_S 49 _t (point)_S 50 _t (although)_S 50 _t (they)_S 49 _t (do)_S 50 _t (not)_S 49 _t (necessarily)_S 50 _t (find)_S 50 _t (a)_S 49 _t (correct)_S 50 _t (\(feasible\))_S 1200 3090 _m (solution.)_S 81 _t (They)_S 82 _t (don't)_S 82 _t (necessarily)_S 81 _t (stop)_S 82 _t (at)_S 82 _t (a)_S 81 _t (solution)_S 82 _t (at)_S 82 _t (all;)_S 81 _t (they)_S 82 _t (most)_S 82 _t (stop)_S 81 _t (at)_S 82 _t (a)_S 82 _t (local)_S 81 _t (minimum)_S 82 _t (of)_S 82 _t (the)_S 1200 2890 _m (objective)_S 76 _t (function.)_S 151 _t (The)_S 76 _t (term)_S 76 _t ("global")_S 76 _t (described)_S 76 _t (here)_S 76 _t (has)_S 75 _t (a)_S 76 _t (different)_S 76 _t (connotation)_S 76 _t (than)_S 76 _t (that)_S 76 _t (for)_S 76 _t (global)_S 1200 2690 _m (optimization;)_S 69 _t (it)_S 69 _t (certainly)_S 69 _t (does)_S 69 _t (not)_S 69 _t (mean)_S 69 _t (that)_S 70 _t (there)_S 69 _t (is)_S 69 _t (any)_S 69 _t (guarantee)_S 69 _t (of)_S 69 _t (finding)_S 69 _t (a)_S 69 _t (solution.)_S 139 _t (Two)_S 69 _t (global)_S 1200 2490 _m (methods)_S 87 _t (are)_S 87 _t (available)_S 87 _t (in)_S 87 _t (NNES;)_S 87 _t (a)_S 87 _t (line)_S 87 _t (search)_S 87 _t (method)_S 86 _t (described)_S 87 _t 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(the)_S 48 _t (strict)_S 49 _t (Newton)_S 48 _t (method.)_S 97 _t (The)_S 49 _t (point)_S 48 _t (generated)_S 49 _t (by)_S 48 _t (equations)_S 49 _t (\(4\))_S 1200 11250 _m (and)_S 59 _t (\(5\),)_S 60 _t /Times-BoldR 550 _ff (x)_S /Times-RomanR 330 _ff 1935 11209 _m (k+1)_S 2107 11209 _m /Times-RomanR 550 _ff 2107 11250 _m (,)_S 59 _t (is)_S 59 _t (not)_S 60 _t (necessarily)_S 59 _t (accepted)_S 59 _t (as)_S 59 _t (a)_S 60 _t (new)_S 59 _t (point;)_S 59 _t (it)_S 59 _t (must)_S 60 _t (meet)_S 59 _t (some)_S 59 _t (acceptance)_S 59 _t (criterion.)_S 119 _t (To)_S 59 _t (do)_S 1200 11050 _m (this,)_S 48 _t (some)_S 48 _t (measure)_S 49 _t (of)_S 48 _t (merit)_S 48 _t (of)_S 49 _t (the)_S 48 _t (current)_S 48 _t (point)_S 49 _t (is)_S 48 _t (required,)_S 48 _t (i.e.,)_S 49 _t (is)_S 48 _t (this)_S 48 _t (point)_S 49 _t (preferred)_S 48 _t (versus)_S 48 _t (the)_S 49 _t (previous)_S 1200 10850 _m (one)_S 68 _t (\(or,)_S 67 _t (possibly,)_S 68 _t (in)_S 67 _t (the)_S 68 _t (case)_S 67 _t 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F8FFFFFFFFFFF87FFFFFFFFFC1 1200 2010 104 _ieq F87FFFFFFFFFF87FFFFFFFFFC1 1200 2009 104 _ieq FC3FFFFFFFFFF0FFFFFFFFFFC1 1200 2008 104 _ieq FE1FFFFFFFFFE1FFFFFFFFFFC1 1208 2007 96 _ieq 8FFFFFFFFF07FFFFFFFFF001 1208 2006 96 _ieq C7FFFFFFFF1FFFFFFFFFF001 1208 2005 96 _ieq F7FFFFFFFFFFFFFFFFFFF001 _s grestore 7658 8417 _m 61 _t 8473 8417 _m 61 _t 61 _t /Times-BoldR 550 _ff (\(13\))_S /Times-RomanR 550 _ff 1200 7306 _m (so)_S 80 _t (for)_S 80 _t (other)_S 80 _t (minimizations\),)_S 79 _t (this)_S 80 _t (usually)_S 80 _t (amounts)_S 79 _t (to)_S 80 _t (a)_S 80 _t (strict)_S 79 _t (decrease)_S 80 _t (in)_S 80 _t (the)_S 80 _t (objective)_S 80 _t (function)_S 79 _t (being)_S gsave 0 0 translate 4 4 scale 100 _gs 100 _gs 833 1811 _m _sp 833 1811 833 1766 834 1766 834 1811 4 _pl _cp _f _s grestore gsave 0 0 translate 4 4 scale 100 _gs 100 _gs 910 1792 _m _sp 910 1792 910 1789 912 1789 913 1789 914 1792 913 1793 912 1794 910 1793 8 _pl _cp _f 100 _gs 100 _gs 911 1792 _m _sp 911 1792 911 1789 913 1789 914 1789 915 1792 914 1793 913 1794 911 1793 8 _pl _cp _f 100 _gs 100 _gs 912 1792 _m _sp 912 1792 912 1789 914 1789 915 1789 916 1792 915 1793 914 1794 912 1793 8 _pl _cp _f _s grestore gsave 0 0 translate 4 4 scale 100 _gs 100 _gs 1010 1811 _m _sp 1010 1811 1010 1766 1011 1766 1011 1811 4 _pl _cp _f _s grestore 1200 7106 _m (required)_S 52 _t (at)_S 52 _t (each)_S 52 _t (step)_S 52 _t (unless)_S 52 _t 3293 7106 _m 3368 7106 _m /Symbol 550 _ff (\321)_S /Times-RomanR 550 _ff (f)_S /Times-BoldR 550 _ff 52 _t 3612 7106 _m 3799 7106 _m 52 _t (s)_S /Times-RomanR 330 _ff 3923 7180 _m (N)_S 4002 7180 _m /Times-RomanR 550 _ff 4002 7106 _m 4077 7106 _m 52 _t (is)_S 52 _t (very)_S 52 _t (large.)_S 104 _t (The)_S 52 _t (Armijo)_S 52 _t (constant)_S 52 _t (is)_S 52 _t (input)_S 52 _t (as)_S 52 _t (ALPHA.)_S 104 _t (Since)_S 52 _t /Symbol 550 _ff (\321)_S /Times-RomanR 550 _ff (f)_S /Times-BoldR 550 _ff gsave 0 0 translate 4 4 scale 100 _gs 100 _gs 307 1742 _m _sp 307 1742 307 1739 309 1739 310 1739 311 1742 310 1743 309 1744 307 1743 8 _pl _cp _f 100 _gs 100 _gs 308 1742 _m _sp 308 1742 308 1739 310 1739 311 1739 312 1742 311 1743 310 1744 308 1743 8 _pl _cp _f 100 _gs 100 _gs 309 1742 _m _sp 309 1742 309 1739 311 1739 312 1739 313 1742 312 1743 311 1744 309 1743 8 _pl _cp _f _s grestore 1200 6906 _m 1388 6906 _m 53 _t (s)_S /Times-RomanR 330 _ff 1512 6980 _m (N)_S 1592 6980 _m /Times-RomanR 550 _ff 1592 6906 _m 52 _t (<)_S 53 _t (0,)_S 52 _t (there)_S 53 _t (must)_S 52 _t (be)_S 53 _t (a)_S 52 _t (range)_S 52 _t (of)_S 53 _t (the)_S 52 _t (relaxation)_S 53 _t (factor,)_S 52 _t /Symbol 550 _ff (l)_S /Times-RomanR 550 _ff (,)_S 53 _t (small)_S 52 _t (enough)_S 53 _t (so)_S 52 _t (that)_S 53 _t (the)_S 52 _t (Armijo)_S 53 _t (criterion)_S 52 _t (can)_S 1200 6706 _m (be)_S 57 _t (met.)_S 115 _t (To)_S 58 _t (find)_S 57 _t (an)_S 58 _t (acceptable)_S 57 _t /Symbol 550 _ff (l)_S /Times-RomanR 550 _ff (,)_S 58 _t (a)_S 57 _t (line)_S 58 _t (search)_S 57 _t (is)_S 58 _t (conducted)_S 57 _t (in)_S 58 _t (which)_S 57 _t /Symbol 550 _ff (l)_S /Times-RomanR 550 _ff 58 _t (is)_S 57 _t (decreased)_S 58 _t (at)_S 57 _t (each)_S 58 _t (step)_S 57 _t (by)_S 58 _t (one)_S 1200 6506 _m (of)_S 61 _t (two)_S 61 _t (mechanisms.)_S 122 _t 1620 6106 _m (The)_S 47 _t (simplest)_S 47 _t (mechanism,)_S 47 _t (the)_S 47 _t (geometric)_S 47 _t (line)_S 47 _t (search,)_S 47 _t (is)_S 47 _t (activated)_S 47 _t (by)_S 47 _t (setting)_S 47 _t (GEOMS)_S 46 _t (to)_S 47 _t (TRUE.)_S 94 _t (After)_S 1200 5906 _m (each)_S 44 _t (failure,)_S 43 _t (i.e.,)_S 44 _t (the)_S 44 _t (objective)_S 44 _t (function)_S 43 _t (at)_S 44 _t (the)_S 44 _t (trial)_S 43 _t (point)_S 44 _t (is)_S 44 _t (not)_S 43 _t (an)_S 44 _t (improvement)_S 44 _t (versus)_S 44 _t (the)_S 43 _t (current)_S 44 _t (objective)_S 1200 5706 _m (function,)_S 61 _t /Symbol 550 _ff (l)_S /Times-RomanR 550 _ff 61 _t (is)_S 61 _t (reduced)_S 61 _t (by)_S 61 _t (a)_S 61 _t (factor,)_S 61 _t /Symbol 550 _ff (s)_S /Times-RomanR 550 _ff (,)_S 61 _t (until)_S 61 _t (the)_S 61 _t (Armijo)_S 61 _t (criterion,)_S 61 _t (equation)_S 61 _t (\(13\),)_S 61 _t (is)_S 61 _t (satisfied,)_S 61 _t (i.e.,)_S 1620 4442 _m (Most)_S 47 _t (commonly,)_S 47 _t (the)_S 47 _t (initial)_S 47 _t (relaxation)_S 48 _t (factor)_S 47 _t (in)_S 47 _t (any)_S 47 _t (iteration,)_S 48 _t (call)_S 47 _t (it)_S 47 _t /Symbol 550 _ff (l)_S /Times-RomanR 330 _ff 6690 4401 _m (0)_S 6745 4401 _m /Times-RomanR 550 _ff 6745 4442 _m (,)_S 47 _t (is)_S 48 _t (1.0,)_S 47 _t (corresponding)_S 47 _t (to)_S 47 _t (a)_S 48 _t (full)_S gsave 0 0 translate 4 4 scale _s 69 1899 325 1246 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale 1144 1306 16 _ieq FC1F 1328 1306 8 _ieq 83 1144 1305 16 _ieq F81F 1328 1305 8 _ieq 03 1144 1304 16 _ieq F00F 1320 1304 16 _ieq FE01 1144 1303 16 _ieq F00F 1320 1303 16 _ieq FE01 1144 1302 16 _ieq F18F 1320 1302 16 _ieq FE31 1144 1301 16 _ieq F18F 1320 1301 16 _ieq FE31 1144 1300 16 _ieq F1CF 1320 1300 16 _ieq FE39 1152 1299 8 _ieq CF 1328 1299 8 _ieq F9 1152 1298 8 _ieq CF 1328 1298 8 _ieq F9 1152 1297 8 _ieq C7 1328 1297 8 _ieq F8 1152 1296 8 _ieq C7 1328 1296 8 _ieq F8 1152 1295 8 _ieq C7 1296 1295 40 _ieq 0001FFFFF8 1152 1294 8 _ieq C7 1288 1294 48 _ieq FE0001FFFFF8 1152 1293 8 _ieq 87 1240 1293 96 _ieq F80001FFFFFFF80001FFFFF0 1152 1292 8 _ieq 87 1240 1292 96 _ieq F80001FFFFFFF07C01FFFFF0 1152 1291 8 _ieq 03 1240 1291 104 _ieq F80001FFFFFFF07E1FFFFFE07F 1152 1290 8 _ieq 03 1288 1290 56 _ieq E0FE0FFFFFE07F 1144 1289 16 _ieq FE03 1288 1289 56 _ieq E0FF0FFFFFC07F 1144 1288 16 _ieq FE03 1288 1288 56 _ieq E0FF07FFFFC07F 1144 1287 16 _ieq FC03 1288 1287 56 _ieq C1FF07FFFF807F 1144 1286 16 _ieq F803 1288 1286 56 _ieq C1FF07FFFF007F 1144 1285 16 _ieq F821 1240 1285 104 _ieq F80001FFFFFFC1FF07FFFF043F 1144 1284 16 _ieq F031 1240 1284 104 _ieq F80001FFFFFFC1FF07FFFE063F 1144 1283 16 _ieq F071 1288 1283 56 _ieq C1FF07FFFE0E3F 1144 1282 16 _ieq E071 1288 1282 56 _ieq C1FF07FFFC0E3F 1144 1281 24 _ieq C0F0C7 1288 1281 104 _ieq C1FF07FFF81E18FFFFFF8FFF87 1144 1280 24 _ieq C0F0C7 1288 1280 120 _ieq E0FF0FFFF81E18FFFFFC0FFC07FF0F 1144 1279 24 _ieq 81F8C7 1288 1279 120 _ieq E0FE0FFFF03F18FFFFFF1FFF0FFF0F 1144 1278 24 _ieq 81F807 1288 1278 120 _ieq F07E1FFFF03F00FFFFFF1FFF0FFE07 1144 1277 24 _ieq 03F807 1288 1277 120 _ieq F0001FFFE07F00FFFFFF1FFF0FFE07 1144 1276 24 _ieq 03FC07 1288 1276 120 _ieq F8003FFFE07F80FFFFFF1FFF0FFE07 1136 1275 32 _ieq FE07FC0F 1288 1275 120 _ieq FC007FFFC0FF81FFFFFE3FFF1FFE07 1152 1274 256 _ieq FE1FFC71FE071FBE3FFFFFFFFFFFFFFFFFFF01FFFFFFFFC3FFC1FE3FC01FFF0F 1168 1273 56 _ieq E060FC001F1C3F 1352 1273 56 _ieq 807E3F801FFF8F 1168 1272 56 _ieq E0C0F8401F1C3F 1352 1272 40 _ieq 1C3C3F1C3F 1168 1271 56 _ieq F890F0C31E1F3F 1344 1271 48 _ieq FE3C3C7E3C3F 1168 1270 56 _ieq F831E1C30E1F3F 1344 1270 48 _ieq FC3C3C7C7C3F 1168 1269 56 _ieq F971C3C78C1E3F 1344 1269 48 _ieq F87C3C787C7F 1168 1268 56 _ieq F0F1C38F881E3F 1344 1268 48 _ieq F87C38F8FC7F 1168 1267 56 _ieq F0E1801F890C7F 1344 1267 48 _ieq F0FC38F0FC7F 1168 1266 48 _ieq F1E380FF810C 1344 1266 48 _ieq F0FC38F1F87F 1168 1265 48 _ieq F1C387FF8309 1344 1265 40 _ieq F0FC70F1F0 1168 1264 48 _ieq E3C287FF8383 1344 1264 48 _ieq F0F8F1A1F0BF 1168 1263 48 _ieq E3C207EF8783 1344 1263 48 _ieq F0F9F181F09F 1168 1262 48 _ieq E3C0878F8787 1344 1262 48 _ieq F0E1E121C01F 1168 1261 48 _ieq C7C1C03F8F87 1344 1261 48 _ieq F803E070103F 1168 1260 48 _ieq C7C1C03F8F8F 1344 1260 48 _ieq F807E0F0307F 1176 1259 40 _ieq E3E0FF9FDF 1344 1259 40 _ieq FC0FF1F871 _s grestore 5756 5223 _m 60 _t 60 _t 60 _t 60 _t 60 _t 60 _t 60 _t 60 _t 60 _t 60 _t 60 _t 60 _t 60 _t 59 _t 59 _t 59 _t 59 _t 59 _t 59 _t 59 _t 59 _t 59 _t 59 _t 59 _t 59 _t 59 _t 59 _t 59 _t 59 _t 59 _t 59 _t 59 _t 59 _t 59 _t 59 _t 59 _t 59 _t 59 _t 59 _t 59 _t 59 _t 59 _t 59 _t 59 _t 59 _t 59 _t 59 _t 59 _t /Times-BoldR 550 _ff (\()_S -2 _t (1)_S -2 _t (4)_S -2 _t (\))_S /Times-RomanR 550 _ff 1200 4242 _m (Newton)_S 53 _t (step)_S 53 _t (although)_S 53 _t (this)_S 53 _t (can)_S 53 _t (be)_S 54 _t (changed)_S 53 _t (in)_S 53 _t (NNES)_S 53 _t (by)_S 53 _t (setting)_S 53 _t (LAM0)_S 53 _t (to)_S 53 _t (a)_S 53 _t (positive)_S 53 _t (number)_S 54 _t (less)_S 53 _t (than)_S 53 _t (1.0.)_S 1200 4042 _m (The)_S 61 _t (standard)_S 61 _t (reduction)_S 61 _t (factor)_S 61 _t (at)_S 61 _t (each)_S 61 _t (step)_S 61 _t (of)_S 61 _t (the)_S 61 _t (line)_S 61 _t (search)_S 61 _t (is)_S 61 _t (2.0,)_S 61 _t (\(thus)_S 61 _t /Symbol 550 _ff (s)_S /Times-RomanR 550 _ff (=0.5\).)_S 122 _t 1620 3842 _m (The)_S 49 _t (other)_S 49 _t (mechanism)_S 49 _t (for)_S 49 _t (reducing)_S 49 _t /Symbol 550 _ff (l)_S /Times-RomanR 550 _ff 49 _t (consists)_S 49 _t (of)_S 49 _t (finding)_S 49 _t (the)_S 49 _t (minimum)_S 49 _t (of)_S 49 _t (a)_S 49 _t (quadratic)_S 49 _t (in)_S 49 _t /Symbol 550 _ff (l)_S /Times-RomanR 550 _ff 50 _t (fit)_S 49 _t (through)_S gsave 0 0 translate 4 4 scale 100 _gs 100 _gs 1356 926 _m _sp 1356 926 1356 923 1358 923 1359 923 1360 926 1359 927 1358 928 1356 927 8 _pl _cp _f 100 _gs 100 _gs 1357 926 _m _sp 1357 926 1357 923 1359 923 1360 923 1361 926 1360 927 1359 928 1357 927 8 _pl _cp _f 100 _gs 100 _gs 1358 926 _m _sp 1358 926 1358 923 1360 923 1361 923 1362 926 1361 927 1360 928 1358 927 8 _pl _cp _f _s grestore 1200 3642 _m (f\()_S /Times-BoldR 550 _ff (x)_S /Times-RomanR 330 _ff 1414 3601 _m (k)_S 1469 3601 _m /Times-RomanR 550 _ff 1469 3642 _m (\))_S 61 _t (and)_S 61 _t (f\()_S /Times-BoldR 550 _ff (x)_S /Times-RomanR 330 _ff 2130 3601 _m (k)_S 2185 3601 _m /Times-RomanR 550 _ff 2185 3642 _m (+)_S /Symbol 550 _ff (l)_S /Times-RomanR 330 _ff 2389 3601 _m (0)_S 2444 3601 _m /Times-BoldR 550 _ff 2444 3642 _m (s)_S /Times-RomanR 330 _ff 2516 3716 _m (N)_S 2595 3716 _m /Times-RomanR 550 _ff 2595 3642 _m (\))_S 61 _t (using)_S 61 _t (the)_S 61 _t (directional)_S 61 _t (derivative,)_S 61 _t /Symbol 550 _ff (\321)_S /Times-RomanR 550 _ff (f)_S /Times-BoldR 550 _ff 61 _t 5398 3642 _m 5586 3642 _m 61 _t (s)_S /Times-RomanR 330 _ff 5718 3716 _m (N)_S 5798 3716 _m /Times-RomanR 550 _ff 5798 3642 _m (,)_S 1200 2162 _m (If)_S 64 _t /Symbol 550 _ff (l)_S /Times-RomanR 330 _ff 1487 2121 _m (min)_S 1658 2121 _m /Times-RomanR 550 _ff 1658 2162 _m 64 _t /Symbol 550 _ff (\316)_S /Times-RomanR 550 _ff 65 _t ([.1)_S /Symbol 550 _ff (l)_S /Times-RomanR 330 _ff 2217 2121 _m (0)_S 2272 2121 _m /Times-RomanR 550 _ff 2272 2162 _m (,.5)_S /Symbol 550 _ff (l)_S /Times-RomanR 330 _ff 2556 2121 _m (0)_S 2611 2121 _m /Times-RomanR 550 _ff 2611 2162 _m (])_S 64 _t (then)_S 64 _t /Symbol 550 _ff (l)_S /Times-RomanR 330 _ff 3216 2121 _m (new)_S 3400 2121 _m /Times-RomanR 550 _ff 3400 2162 _m 64 _t (=)_S 65 _t /Symbol 550 _ff (l)_S /Times-RomanR 330 _ff 3733 2121 _m (min)_S 3904 2121 _m /Times-RomanR 550 _ff 3904 2162 _m (.)_S 128 _t (Otherwise)_S 64 _t /Symbol 550 _ff (l)_S /Times-RomanR 330 _ff 4996 2121 _m (new)_S 5179 2121 _m /Times-RomanR 550 _ff 5179 2162 _m 65 _t (is)_S 64 _t (the)_S 64 _t (nearest)_S 64 _t (end-point.)_S 65 _t (Similarly,)_S 64 _t (for)_S 64 _t (subsequent)_S gsave 0 0 translate 4 4 scale _s 155 1899 325 668 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale 1304 814 16 _ieq FE0F 1304 813 144 _ieq FC07FFFFFFFFFFFFFFF00007FFFFFF80FC03 1304 812 144 _ieq F803FFFFFFFFFFFFFFF00007FFFFFF00FC07 1304 811 144 _ieq F001FFFFFFFFFFFFFFF1C1C7FFFFFFE07F1F 1304 810 144 _ieq F3C1FFFFFFFFFFFFFFE383CFFFFFFFE07F3F 1304 809 144 _ieq E7F0FFFFFFFFFFFFFFE783CFFFFFFFE03F3F 1304 808 144 _ieq E7F0FFFFFFFFFFFFFFEF83CFFFFFFFE03F3F 1304 807 144 _ieq EFF0FFFFFFFFFFFFFFFF83FFFFFFFFC01E3F 1272 806 176 _ieq 83FFFFFFFFF0FFFFFFFFFFFE03FF07FFFFFFFFC81E7F 1272 805 176 _ieq 03FFFFFFFFF0FF00000007FC01FF07FFFFFFFFCC1E7F 1264 804 184 _ieq FE01FFFFFFFFF1FF00000007FC61FF07FFFFFFFFCC0E7F 1264 803 184 _ieq FE01FFFFFFFFF3FF8000000FF841FF07FFFFFFFF8E0C7F 1264 802 176 _ieq FE31FFFFFFFFE7FF83FFFF0FF0C1FE0FFFFFFFFF9E04 1264 801 176 _ieq FE31FFFFFFFFEFFFC1FFFF1FE0E3FE0FFFFFFFFF9F04 1264 800 176 _ieq FE39FFFFFFFF9FFFC1FFFF1FE1FFFE0FFFFFFFFF9F00 1272 799 168 _ieq F9FFFFFFFF3FFFE0FFFF3FC1FFFE0FFFFFFFFF1F80 1272 798 168 _ieq F9FFFFFFFE7F7FE0FFFE3FC1FFFC1FFFFFFFFF3F81 1272 797 168 _ieq F8FFFFFFFCFE7FE07FFE3FC1FFFC1FFFFFFFFF3FC1 1272 796 168 _ieq F8FFFFFFF8007FF07FFC7FC3FFFC3FFF873FFF3FC1 1272 795 168 _ieq F8FFFFFFF000FFF07FFC78001FFC3FFF003FFE3FE1 1272 794 168 _ieq F8FFFFFFE000FFF83FF8F8001FE007FE003FF80FE3 1272 793 168 _ieq F0FFFFFFE001FFF83FF8F0003FE00FFC383FF80FF3 1272 792 168 _ieq F0FFFFFFFFFFFFFC1FF1FF07FFFFFFFC3C3FFFFFF3 1272 791 144 _ieq E07FFFFFFFFFFFFC1FF1FF0FFFFFFFF83E3F 1272 790 144 _ieq E07FFFFFFFFFFFFE0FF3FF0FFFFFFFF81E3F 1272 789 144 _ieq C07FFFFFFFFFFFFE0FE3FE0FFFFFFFF81E3F 1272 788 136 _ieq C07FFFFFFFFFFFFE07E3FE0FFFFFFFF80F 1272 787 136 _ieq 807FFFFFFFFFFFFF07C7FE1FFFFFFFFC07 1272 786 136 _ieq 007FFFFFFFFFFFFF07C7FE1FFFFFFFFE03 1272 785 136 _ieq 043FFFFFFFFFFFFF838FFC1FFFFFFFFE03 1264 784 144 _ieq FE063FFFFFFFFFFFFF838FFC1FFFFFFFFF01 1264 783 144 _ieq FE0E3FFFFFFFFFFFFFC11FFC3FFFFFFFFF01 1264 782 144 _ieq FC0E3FFF01FFFFFFFFC11FFC3FFFFFFFE780 1264 781 144 _ieq F81E18FE00FFFFFFFFC01FF83FFFFFFFE7C0 1264 780 144 _ieq F81E18FE00FFFFFFFFE03FF83FFFFFFFE7E0 1264 779 144 _ieq F03F18FC387FFFFFFFE03FF83FFFFFFFE3E0 1264 778 144 _ieq F03F00FC7C7FFFFFFFF07FF83FFFFFFFE3E0 1264 777 144 _ieq E07F00F8FC3FFFFFFFF07FF07FFFFFFFC1E1 1264 776 144 _ieq E07F80F8FE3FFFFFFFF8FFF07FFFFFFFC003 1264 775 144 _ieq C0FF81F0FE1FFFFFFFF8FFF0FFFFFFFFC003 1280 774 128 _ieq C3F0FE1FFFFFFFFDFFF0FFFFFFFFCE07 1288 773 120 _ieq F0FE1FFFFFFFFDFFF0FFFFFFFFFF0F 1288 772 72 _ieq F0FE1FFFFFFFFFFFF1 1288 771 72 _ieq F0FE1FFFFFFFFFFFE1 808 770 8 _ieq 83 1288 770 72 _ieq F0FE1FFFFFFFFFFFC3 808 769 8 _ieq 03 1288 769 72 _ieq F0FE1FFFFFFFFFE1C3 800 768 16 _ieq FE01 1288 768 72 _ieq F0FE1FFFFFFFFFC183 800 767 16 _ieq FE01 1288 767 72 _ieq F0FE1FFFFFFFFFC103 800 766 16 _ieq FE31 1288 766 72 _ieq F8FE3FFFFFFFFFC00F 800 765 16 _ieq FE31 1288 765 72 _ieq F87C3FFFFFFFFFC01F 800 764 16 _ieq FE39 1288 764 72 _ieq F87C3FFFFFFFFFE07F 808 763 8 _ieq F9 1288 763 24 _ieq FC387F 808 762 8 _ieq F9 1288 762 24 _ieq FE007F 808 761 8 _ieq F8 1296 761 8 _ieq 00 808 760 8 _ieq F8 1296 760 8 _ieq 83 808 759 8 _ieq F8 808 758 8 _ieq F8 808 757 8 _ieq F0 896 757 24 _ieq FC0000 808 756 8 _ieq F0 896 756 24 _ieq FC0000 808 755 112 _ieq E07FFFFFFFFFFFFFFFFFFFFC0000 808 754 16 _ieq E07F 808 753 16 _ieq C07F 944 753 24 _ieq F80001 808 752 16 _ieq C07F 944 752 24 _ieq F80001 808 751 16 _ieq 807F 808 750 16 _ieq 007F 808 749 912 _ieq 043FFFFFFFFFFFFFFFFFFFFC0000FFFFFFFFFFFFFFFF000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001F 800 748 920 _ieq 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FE3F 1152 2359 8 _ieq F3 1152 2358 8 _ieq F3 1152 2357 8 _ieq F9 1152 2356 8 _ieq F9 1152 2355 8 _ieq F8 1152 2354 16 _ieq FC7F 1152 2353 16 _ieq FE1F 1160 2352 8 _ieq 07 1160 2351 8 _ieq 87 _s grestore 8595 9677 _m /Times-BoldR 550 _ff (\(20\))_S /Times-RomanR 550 _ff 1200 8642 _m (objective)_S 69 _t (function)_S 70 _t (values,)_S 70 _t (NNES)_S 69 _t (uses)_S 70 _t (a)_S 69 _t (more)_S 70 _t (aggressive)_S 69 _t (version)_S 70 _t (of)_S 70 _t (the)_S 69 _t (same)_S 70 _t (procedure)_S 70 _t (because)_S 69 _t (of)_S 70 _t (its)_S 1200 8442 _m (nonmonotonic)_S 61 _t (searches:)_S 1200 7162 _m (The)_S 52 _t (choice)_S 53 _t (of)_S 52 _t (starting)_S 52 _t (at)_S 53 _t (at)_S 52 _t (a)_S 53 _t (user-supplied)_S 52 _t /Symbol 550 _ff (l)_S /Times-RomanR 330 _ff 4520 7121 _m (0)_S 4575 7121 _m /Times-RomanR 550 _ff 4575 7162 _m 53 _t (or)_S 52 _t (using)_S 53 _t (Deuflhard's)_S 52 _t (method)_S 53 _t (is)_S 52 _t (set)_S 52 _t (by)_S 53 _t (DEUFLH)_S 52 _t (which)_S 53 _t (has)_S gsave 0 0 translate 4 4 scale _s 145 1899 325 1928 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale 1152 2063 8 _ieq 3F 1144 2062 16 _ieq FC3F 1144 2061 8 _ieq F9 1144 2060 8 _ieq FB 1144 2059 8 _ieq F3 1144 2058 8 _ieq E7 1144 2057 8 _ieq CF 1144 2056 8 _ieq CF 1144 2055 8 _ieq 9F 1144 2054 8 _ieq 9F 1144 2053 8 _ieq 1F 1144 2052 8 _ieq 1F 1144 2051 8 _ieq 1F 1144 2050 8 _ieq 1F 1144 2049 8 _ieq 1F 1144 2048 24 _ieq 1FFFF9 1304 2048 16 _ieq C07F 1440 2048 48 _ieq F83FFFFFFFCF 1144 2047 24 _ieq 1FFFE1 1288 2047 32 _ieq 0FFF803F 1440 2047 48 _ieq E00FFFFFFF0F 1144 2046 24 _ieq 1FFF81 1280 2046 40 _ieq FE07FF0C3F 1440 2046 48 _ieq 8003FFFFFC0F 1144 2045 24 _ieq 1FFE01 1280 2045 40 _ieq FE07FE083F 1440 2045 48 _ieq 8F83FFFFF00F 1144 2044 24 _ieq 1FF801 1280 2044 40 _ieq FE07FC183F 1440 2044 48 _ieq 0FC1FFFFC00F 1144 2043 24 _ieq 1FF841 1288 2043 32 _ieq 0FFC1C7F 1432 2043 56 _ieq FE1FE0FFFFC20F 1144 2042 24 _ieq 1FFFC1 1296 2042 16 _ieq F83F 1392 2042 96 _ieq 3FFFFFFFFFFC1FE07FFFFE0F 1144 2041 24 _ieq 1FFFC1 1296 2041 16 _ieq F83F 1392 2041 96 _ieq 0FFFFFFFFFFC3FF07FFFFE0F 1144 2040 24 _ieq 1FFFC1 1296 2040 16 _ieq F83F 1392 2040 96 _ieq 03FFFFFFFFF83FF07FFFFE0F 1144 2039 24 _ieq 1FFFC1 1296 2039 16 _ieq F83F 1392 2039 96 _ieq 00FFFFFFFFF83FF07FFFFE0F 1144 2038 24 _ieq 1FFFC1 1280 2038 32 _ieq FE0FF87F 1392 2038 96 _ieq 001FFFFFFFF03FF03FFFFE0F 1144 2037 24 _ieq 1FFFC1 1280 2037 208 _ieq E00F0003FFFFF0FF07FFFFFFFFFFC007FFFFFFF03FF03FFFFE0F 1144 2036 24 _ieq 1FFFC1 1280 2036 208 _ieq E01F0003FFFFF0FF07FFFFFFFFFFF801FFFFFFF03FF03FFFFE0F 1144 2035 24 _ieq 1FFFC1 1280 2035 208 _ieq FC1E0007FFFFF0FF07FFFFFFFFFFFE007FFFFFF03FF03FFFFE0F 1144 2034 24 _ieq 1FFFC1 1280 2034 208 _ieq FC1FE0FFFFFFF0FF07FFFFFFFFFFFFC01FFFFFF03FF03FFFFE0F 1144 2033 24 _ieq 1FFFC1 1280 2033 208 _ieq FC3FE1FFFFFFF0FF07FFFFFFFFFFFFF807FFFFF03FF03FFFFE0F 1144 2032 24 _ieq 1FFFC1 1280 2032 208 _ieq F83FE1FFFFFFF0FF07FFFFFFFFFFFFFE07FFFFF03FF03FFFFE0F 1144 2031 24 _ieq 1FFFC1 1280 2031 208 _ieq F83FC1FFFFFFF0FF07FFFFFFFFFFFFF807FFFFF03FF03FFFFE0F 1144 2030 24 _ieq 1FFFC1 1280 2030 208 _ieq F83FC1FFFFFFF0FF07FFFFFFFFFFFFE007FFFFF03FF03FFFFE0F 1144 2029 24 _ieq 1FFFC1 1280 2029 208 _ieq F07FC3FFFFFFF0FF07FFFFFFFFFFFF001FFFFFF03FF03FFFFE0F 1144 2028 24 _ieq 1FFFC1 1280 2028 208 _ieq F07FC3FFFFFFF0FF07FFFFFFFFFFFC007FFFFFF03FF03FFFFE0F 1144 2027 24 _ieq 1FFFC1 1280 2027 208 _ieq F07F83FFFFFFF0FF07FFFFFFFFFFF003FFFFFFF83FF03FFFFE0F 1144 2026 24 _ieq 1FFFC1 1280 2026 208 _ieq F0FF83FFFFFFF0FF07FFFFFFFFFFC00FFFFFFFF83FF03FFFFE0F 1144 2025 24 _ieq 1FFFC1 1280 2025 208 _ieq E0FF87FFFFFFF0FF07FFFFFFFFFF007FFFFFFFFC1FF03FFFFE0F 1144 2024 24 _ieq 1FFFC1 1280 2024 208 _ieq E0FF87FFFFFFF0FF07FFFFFFFFFF01FFFFFFFFFC1FF07FFFFE0F 1144 2023 24 _ieq 1FFFC1 1280 2023 208 _ieq E1FF07FFFFFFF0FF047FE3FFFFFF0FFFFFFFFFFC1FE07FFFFE0F 1144 2022 24 _ieq 1FFFC1 1280 2022 208 _ieq C1CF07FFFFFFF07F047E03FFFFFF3FFFFFFFFFFC0FE07C3FFE0F 1144 2021 24 _ieq 1FFFC1 1280 2021 208 _ieq C18F07FFFFFFF07E047F87FFFFFFFFFFFFFFFFFC0FE0FC3FFE0F 1144 2020 24 _ieq 1FFFC1 1280 2020 208 _ieq C19F07FFFFFFF01C007F87FFFFFFFFFFFFFFFFFE07C1F81FFE0F 1144 2019 24 _ieq 1FFFC0 1280 2019 208 _ieq C01E0FFFFFFFF000007F87FFFFFFFFFFFFFFFFFF0781F81FFE07 1144 2018 32 _ieq 1FFC001F 1280 2018 208 _ieq C03E0FFFFFFFF000007F87FFFFFFFFFFFFFFFFFFC003F81FE000 1144 2017 32 _ieq 1FFC001F 1280 2017 208 _ieq C07E1FFFFFFFF08080FF0FFFFFFFFFFFFFFFFFFFC007F81FE000 1144 2016 8 _ieq 1F 1280 2016 192 _ieq E0FE1FFFFFFFF0C1C1FF0FFFFFFFFFFFFFFFFFFFE00FFC3F 1144 2015 8 _ieq 1F 1280 2015 192 _ieq F1FE1FFFFFFFF0FFFFFF001FFFFFFFFFFFFFFFFFF01FFE3F 1144 2014 8 _ieq 1F 1288 2014 88 _ieq FE3FFFFFFFF0FFFFFF1C3F 1144 2013 8 _ieq 1F 1288 2013 80 _ieq FC3FFFFFFFF0FFFFFE18 1144 2012 8 _ieq 1F 1288 2012 80 _ieq F87FFFFFFFF0FFFFFE13 1032 2011 8 _ieq 83 1144 2011 8 _ieq 1F 1280 2011 88 _ieq FC387FFFFFFFF0FFFFFE03 1032 2010 8 _ieq 03 1144 2010 8 _ieq 1F 1280 2010 88 _ieq F8307FFFFFFFF0FFFFFC07 1024 2009 16 _ieq FE01 1144 2009 8 _ieq 1F 1280 2009 88 _ieq F8207FFFFFFFF0FFFFFC07 1024 2008 16 _ieq FE01 1144 2008 8 _ieq 1F 1280 2008 88 _ieq F801FFFFFFFFF0FFFFFC47 1024 2007 16 _ieq FE31 1144 2007 8 _ieq 3F 1280 2007 88 _ieq F803FFFFFFFFF0FFFFF867 1024 2006 16 _ieq FE31 1144 2006 8 _ieq 3F 1280 2006 96 _ieq FC0FFFFFFFFFFFFFFFF863BF 1024 2005 16 _ieq FE39 1136 2005 16 _ieq FE7F 1352 2005 24 _ieq F861BF 1032 2004 8 _ieq F9 1136 2004 16 _ieq FE7F 1352 2004 24 _ieq F8E13F 1032 2003 8 _ieq F9 1136 2003 16 _ieq FC7F 1352 2003 24 _ieq F0E07F 1032 2002 8 _ieq F8 1136 2002 8 _ieq F8 1352 2002 24 _ieq F0F07F 1032 2001 8 _ieq F8 1136 2001 8 _ieq F0 1360 2001 8 _ieq F8 1032 2000 8 _ieq F8 1136 2000 8 _ieq C1 1032 1999 8 _ieq F8 1128 1999 16 _ieq FE03 1032 1998 112 _ieq F0FFFFFFFFFFFFFC0000FFFFFE07 1032 1997 112 _ieq F0FFFFFFFFFFFFFC0000FFFFFFC7 1032 1996 112 _ieq E07FFFFFFFFFFFFC0000FFFFFFE3 1032 1995 16 _ieq E07F 1136 1995 8 _ieq F1 1032 1994 16 _ieq C07F 1136 1994 8 _ieq F8 1032 1993 16 _ieq C07F 1136 1993 16 _ieq F87F 1032 1992 16 _ieq 807F 1136 1992 16 _ieq FC7F 1032 1991 120 _ieq 007FFFFFFFFFFFFC0000FFFFFFFE7F 1032 1990 120 _ieq 043FFFFFFFFFFFFC0000FFFFFFFE7F 1024 1989 128 _ieq FE063FFFFFFFFFFFFC0000FFFFFFFF3F 1024 1988 24 _ieq FE0E3F 1144 1988 8 _ieq 3F 1024 1987 40 _ieq FC0E3FFF01 1144 1987 64 _ieq 1FFFC1FFFFFFFE7F 1304 1987 8 _ieq 80 1440 1987 48 _ieq FC1FFFFFFFE7 1024 1986 40 _ieq F81E18FE00 1144 1986 176 _ieq 1FFF007FFFFFF87FFFFFFFFFFFFFFFFFFFFE1FFF007F 1440 1986 48 _ieq F007FFFFFF87 1024 1985 40 _ieq F81E18FE00 1144 1985 176 _ieq 1FFC001FFFFFE07FFFFFFFFFFFFFFFFFFFFC0FFE187F 1440 1985 88 _ieq C001FFFFFE07FFFFFFF87F 1024 1984 296 _ieq F03F18FC387FFFFFFFFFFFFFFFFFFF1FFC7C1FFFFF807FFFFFFFFFFFFFFFFFFFFC0FFC107F 1440 1984 88 _ieq C7C1FFFFF807FFFFFFF87F 1024 1983 296 _ieq F03F00FC7C7FFFFFFFFFFFFFFFFFFF1FF87E0FFFFE007FFFFFFFFFFFFFFFFFFFFC0FF8307F 1440 1983 88 _ieq 87E0FFFFE007FFFFFFF03F 1024 1982 288 _ieq E07F00F8FC3FFFFFFFFFFFFFFFFFFF1FF0FF07FFFE107FFFFFFFFFFFFFFFFFFFFE1FF838 1440 1982 88 _ieq 0FF07FFFE107FFFFFFF03F 1024 1981 184 _ieq E07F80F8FE3FFFFFFFFFFFFFFFFFFF1FE0FF03FFFFF07F 1296 1981 16 _ieq F07F 1432 1981 96 _ieq FE0FF03FFFFF07FFFFFFF03F 1024 1980 184 _ieq C0FF81F0FE1FFFFFFFFFFFFFFFFFFF1FE1FF83FFFFF07F 1296 1980 16 _ieq F07F 1432 1980 96 _ieq FE1FF83FFFFF07FFFFFFF03F 1040 1979 168 _ieq C3F0FE1FFFFFFFFFFFFFFFFFFF1FC1FF83FFFFF07F 1296 1979 16 _ieq F07F 1432 1979 96 _ieq FC1FF83FFFFF07FFFFFFF87F 1048 1978 160 _ieq F0FE1FFFFFFFFFFFFFFFFFFF1FC1FF83FFFFF07F 1296 1978 16 _ieq F07F 1408 1978 120 _ieq EFFFFFFC1FF83FFFFF07FFFFFFFC7F 1048 1977 256 _ieq F0FE1FFFFFFFFFFFFFFFFFFF1F81FF81FFFFF07FFFFFFFFFFFFFFFFFFFFC1FF0 1408 1977 80 _ieq 8FFFFFF81FF81FFFFF07 1048 1976 440 _ieq F0FE1FFFFFFFFFFFFFFFFFFF1F81FF81FFFFF07FFFFFFFFFFFFFFFFFFFC01E0007FFFFE1FE0FFFFFFFFFFFFFFE07FFFFF81FF81FFFFF07 1048 1975 440 _ieq F0FE1FFFFFFFFFFFFFFFFFFF1F81FF81FFFFF07FFFFFFFFFFFFFFFFFFFC03E0007FFFFE1FE0FFFFFFFFFFFFFF81FFFFFF81FF81FFFFF07 1048 1974 440 _ieq F0FE1FFFFFFFFFFFFFFFFFFF1F81FF81FFFFF07FFFFFFFFFFFFFFFFFFFF83C000FFFFFE1FE0FFFFFFFFFFFFFE07FFFFFF81FF81FFFFF07 1048 1973 440 _ieq F0FE1FFFFFFFFFFFFFFFFFFF1F81FF81FFFFF07FFFFFFFFFFFFFFFFFFFF83FC1FFFFFFE1FE0FFFFFFFFFFFFF81FFFFFFF81FF81FFFFF07 1048 1972 440 _ieq F0FE1FFFFFFFFFFFFFFFFFFF1F81FF81FFFFF07FFFFFFFFFFFFFFFFFFFF87FC3FFFFFFE1FE0FFFFFFFFFFFFE07FFFFFFF81FF81FFFFF07 1048 1971 440 _ieq F8FE3FFFFFFFFFFFFFFFFFFF1F81FF81FFFFF07FFFFFFFFFFFFFFFFFFFF07FC3FFFFFFE1FE0FFFFFFFFFFFF81FFFFFFFF81FF81FFFFF07 1048 1970 440 _ieq F87C3FFFFFFFFFFFFFFFFFFF1F81FF81FFFFF07FFFFFFFFFFFFFFFFFFFF07F83FFFFFFE1FE0FFFFFFFFFFFE07FFFFFFFF81FF81FFFFF07 1048 1969 440 _ieq F87C3FFFFFFFFFFFFFFFFFFF1F81FF81FFFFF07FFFFFFFFFFFFFFFFFFFF07F83FFFFFFE1FE0FFFFFFFFFFFC1FFFFFFFFF81FF81FFFFF07 1048 1968 440 _ieq FC387FFFFFFFFFFFFFFFFFFF1F81FF81FFFFF07FFFFFFFFFFFFFFFFFFFE0FF87FFFFFFE1FE0FFFFFFFFFFFE0FFFFFFFFF81FF81FFFFF07 1048 1967 440 _ieq FE007FFFFFFFFFFFFFFFFFFF1F81FF81FFFFF07FFFFFFFFFFFFFFFFFFFE0FF87FFFFFFE1FE0FFFFFFFFFFFF83FFFFFFFF81FF81FFFFF07 1056 1966 8 _ieq 00 1144 1966 344 _ieq 1FC1FF81FFFFF07FFFFFFFFFFFFFFFFFFFE0FF07FFFFFFE1FE0FFFFFFFFFFFFE0FFFFFFFFC1FF81FFFFF07 1056 1965 8 _ieq 83 1144 1965 344 _ieq 1FC1FF81FFFFF07FFFFFFFFFFFFFFFFFFFE1FF07FFFFFFE1FE0FFFFFFFFFFFFF03FFFFFFFC1FF81FFFFF07 1144 1964 344 _ieq 1FE0FF81FFFFF07FFFFFFFFFFFFFFFFFFFC1FF0FFFFFFFE1FE0FFFFFFFFFFFFFC0FFFFFFFE0FF81FFFFF07 1144 1963 344 _ieq 1FE0FF83FFFFF07FFFFFFFFFFFFFFFFFFFC1FF0FFFFFFFE1FE0FFFFFFFFFFFFFF03FFFFFFE0FF83FFFFF07 1144 1962 344 _ieq 1FE0FF03FFFFF07FFFFFFFFFFFFFFFFFFFC3FE0FFFFFFFE1FE08FFC7FFFFFFFFFC0FFFFFFE0FF03FFFFF07 1144 1961 344 _ieq 1FE07F03E1FFF07FFFFFFFFFFFFFFFFFFF839E0FFFFFFFE0FE08FC07FFFFFFFFFE07FFFFFE07F03E1FFF07 1144 1960 344 _ieq 1FE07F07E1FFF07FFFFFFFFFFFFFFFFFFF831E0FFFFFFFE0FC08FF0FFFFFFFFFFF87FFFFFE07F07E1FFF07 1144 1959 344 _ieq 1FF03E0FC0FFF07FFFFFFFFFFFFFFFFFFF833E0FFFFFFFE03800FF0FFFFFFFFFFFEFFFFFFF03E0FC0FFF07 1144 1958 344 _ieq 1FF83C0FC0FFF03FFFFFFFFFFFFFFFFFFF803C1FFFFFFFE00000FF0FFFFFFFC00007FFFFFF83C0FC0FFF03 1144 1957 352 _ieq 1FFE001FC0FF0007FFFFFFFFFFFFFFFFFF807C1FFFFFFFE00000FF0FFFFFFFC00007FFFFFFE001FC0FF0007F 1144 1956 352 _ieq 1FFE003FC0FF0007FFFFFFFFFFFFFFFFFF80FC3FFFFFFFE10101FE1FFFFFFFC00007FFFFFFE003FC0FF0007F 1144 1955 40 _ieq 1FFF007FE1 1280 1955 192 _ieq C1FC3FFFFFFFE18383FE1FFFFFFFFFFFFFFFFFFFF007FE1F 1144 1954 40 _ieq 1FFF80FFF1 1280 1954 192 _ieq E3FC3FFFFFFFE1FFFFFE003FFFFFFFFFFFFFFFFFF80FFF1F 1144 1953 8 _ieq 1F 1288 1953 88 _ieq FC7FFFFFFFE1FFFFFE387F 1144 1952 8 _ieq 1F 1288 1952 80 _ieq F87FFFFFFFE1FFFFFC31 1144 1951 8 _ieq 1F 1288 1951 80 _ieq F0FFFFFFFFE1FFFFFC27 1144 1950 8 _ieq 1F 1280 1950 88 _ieq F870FFFFFFFFE1FFFFFC07 1144 1949 8 _ieq 1F 1280 1949 88 _ieq F060FFFFFFFFE1FFFFF80F 1144 1948 8 _ieq 1F 1280 1948 88 _ieq F040FFFFFFFFE1FFFFF80F 1144 1947 8 _ieq 1F 1280 1947 88 _ieq F003FFFFFFFFE1FFFFF88F 1144 1946 8 _ieq 1F 1280 1946 88 _ieq F007FFFFFFFFE1FFFFF0CF 1144 1945 8 _ieq 1F 1280 1945 96 _ieq F81FFFFFFFFFFFFFFFF0C77F 1144 1944 8 _ieq 1F 1352 1944 24 _ieq F0C37F 1144 1943 8 _ieq 1F 1352 1943 24 _ieq F1C27F 1144 1942 8 _ieq 1F 1352 1942 16 _ieq E1C0 1144 1941 8 _ieq 1F 1352 1941 16 _ieq E1E0 1144 1940 8 _ieq 9F 1360 1940 8 _ieq F1 1144 1939 8 _ieq 9F 1144 1938 8 _ieq 9F 1144 1937 8 _ieq CF 1144 1936 8 _ieq CF 1144 1935 8 _ieq C7 1144 1934 8 _ieq E3 1144 1933 8 _ieq F0 1144 1932 16 _ieq F83F 1144 1931 16 _ieq FC3F _s grestore 8595 7997 _m /Times-BoldR 550 _ff (\(21\))_S /Times-RomanR 550 _ff 1200 6962 _m (the)_S 61 _t (default)_S 61 _t (of)_S 61 _t (TRUE;)_S 61 _t (in)_S 61 _t (general,)_S 61 _t (Deuflhard's)_S 61 _t (method)_S 61 _t (is)_S 61 _t (slightly)_S 61 _t (faster.)_S 1620 6562 _m (Deuflhard)_S 77 _t (\(1974,)_S 77 _t (1975\))_S 76 _t (also)_S 77 _t (proposed)_S 76 _t (a)_S 77 _t (second)_S 76 _t (step)_S 77 _t (acceptance)_S 76 _t (criterion,)_S 77 _t (known)_S 76 _t (as)_S 77 _t (the)_S 76 _t /Times-ItalicR 550 _ff (natural)_S /Times-RomanR 550 _ff 1200 6362 _m (objective)_S 61 _t (function,)_S 61 _t (based)_S 61 _t (on)_S 61 _t /Times-BoldR 550 _ff 3384 6362 _m (s)_S 3374 6362 _m _U /Symbol 550 _ff (`)_S 3374 6362 _m /Times-BoldR 550 _ff 92 _t 3465 6362 _m /Times-RomanR 550 _ff (.)_S 61 _t 1200 5514 _m (This)_S 54 _t (criterion)_S 54 _t (can)_S 55 _t (be)_S 54 _t (used)_S 54 _t (as)_S 55 _t (well)_S 54 _t (as)_S 54 _t (the)_S 55 _t (function)_S 54 _t (value)_S 55 _t (criterion,)_S 54 _t /Times-ItalicR 550 _ff (f)_S /Times-RomanR 550 _ff (,)_S 54 _t (but)_S 55 _t (not)_S 54 _t (alone,)_S 54 _t (by)_S 55 _t (setting)_S 54 _t (ACPTCR)_S 55 _t (to)_S gsave 0 0 translate 4 4 scale _s 82 1899 325 1471 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale 1256 1543 32 _ieq FC07E01F 1256 1542 32 _ieq F807E03F 1264 1541 16 _ieq 03F8 1264 1540 16 _ieq 03F9 1264 1539 16 _ieq 01F9 1264 1538 16 _ieq 01F9 1024 1537 72 _ieq 00000000000000001F 1256 1537 24 _ieq FE00F1 1024 1536 72 _ieq 00000000000000001F 1256 1536 24 _ieq FE40F3 1024 1535 72 _ieq 00000000000000001F 1256 1535 24 _ieq FE60F3 1256 1534 24 _ieq FE6073 1256 1533 24 _ieq FC7063 1256 1532 24 _ieq FCF027 1256 1531 24 _ieq FCF827 936 1530 16 _ieq C07F 1256 1530 24 _ieq FCF807 912 1529 104 _ieq F8007F803FFFFFFFFFFFFFF39F 1104 1529 16 _ieq F9CF 1208 1529 96 _ieq CE7FFFFFFFFFF8FC07FFFF9C 912 1528 104 _ieq F8007F8C3FFFFFFFFFFFFFF39F 1104 1528 16 _ieq F9CF 1208 1528 96 _ieq CE7FFFFFFFFFF9FC0FFFFF9C 920 1527 96 _ieq 01FF083FFFFFFFFFFFFFF39F 1104 1527 16 _ieq F9CF 1208 1527 96 _ieq CE7FFFFFFFFFF9FE0FFFFF9C 920 1526 96 _ieq 03FE183FFFFFFFFFFFFFF39F 1104 1526 16 _ieq F9CF 1208 1526 96 _ieq CE7FFFFFFFFFF9FE0FFFFF9C 920 1525 96 _ieq 03FC1C7FFFFFFFFFFFFFF39F 1104 1525 16 _ieq F9CF 1208 1525 96 _ieq CE7FFFFFFFFFF1FF0FFFFF9C 920 1524 96 _ieq 03FC3FFFFFFFFFFFFFFFF39F 1104 1524 16 _ieq F9CF 1208 1524 96 _ieq CE7FFFFFFFFFC07F1FFFFF9C 1520 1524 56 _ieq 3FFFFFFFFFFFCF 912 1523 104 _ieq FE07F83FFFFFFFFFFFFFFFF39F 1104 1523 16 _ieq F9CF 1208 1523 96 _ieq CE7FFFFFFFFFC07F9FFFFF9C 1512 1523 64 _ieq FE3FFFFFFFFFFF8F 912 1522 104 _ieq FE07F83FFFFFFFFFFFFFFFF39F 1104 1522 16 _ieq F9CF 1208 1522 96 _ieq CE7FFFFFFFFFFFFF9FFFFF9C 1512 1522 64 _ieq FC3FFFFFFFFFFF0F 912 1521 104 _ieq FC0FF83FFFFFFFFFFFFFFFF39F 1104 1521 200 _ieq F9CFFFFFFFFFFFFFFFBFFFFFFFCE7FFFFFFFFFFFFFFFFFFF9C 1512 1521 64 _ieq F87FFFFFFFFFFE1F 912 1520 392 _ieq FC0FF87FF0FFFFFFFFFFFFF39FFFFF0E7FFFFFFFFFFFFFFFF9CFFFFFFFFFFFFFFE3FFFFFFFCE7FFFFC39FFFFFFFFFFFF9C 1408 1520 208 _ieq FC0FFFFC1FFFC1FFFF0FFC1C1FF07FFFFFFE0F3C1FFFC3FF0707 912 1519 392 _ieq FC0F0003E07FFFFFFFFFFFF39FFFFE007FFFFFFFFFFFFFFFF9CFFFFFFFFFFFFFF81FFFFFFFCE7FFFF801FFFFFFFFFFFF9C 1408 1519 208 _ieq F8007FF007FF007FFC03C0100FC007FFFFF8003001FF00F00403 912 1518 392 _ieq FC0F0003E07FFFFFFFFFFFF39FFFFC007FFFFFFFFFFFFFFFF9CFFFFFFFFFFFFFF03FFFFFFFCE7FFFF001FFFFFFFFFFFF9C 1408 1518 208 _ieq F0007FC003FC003FF001C020070007FFFFF0000001FC00700801 912 1517 392 _ieq 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/Times-BoldR 550 _ff (x)_S /Times-RomanR 330 _ff 8563 6561 _m (k)_S 8618 6561 _m /Times-RomanR 550 _ff 8618 6602 _m 64 _t (+)_S 64 _t /Times-BoldR 550 _ff (s)_S /Times-RomanR 330 _ff 8921 6676 _m (N)_S /Times-RomanR 550 _ff 1200 6402 _m (is)_S 65 _t (within)_S 66 _t (the)_S 65 _t (trust)_S 65 _t (region;)_S 65 _t /Times-BoldR 550 _ff (x)_S /Times-RomanR 330 _ff 3278 6361 _m (k)_S 3333 6361 _m /Times-RomanR 550 _ff 3333 6402 _m 66 _t (+)_S 65 _t /Times-BoldR 550 _ff (s)_S /Times-RomanR 330 _ff 3639 6476 _m (CP)_S 3773 6476 _m /Times-RomanR 550 _ff 3773 6402 _m 65 _t (is)_S 65 _t (outside)_S 66 _t (the)_S 65 _t (trust)_S 65 _t (region)_S 66 _t (or,)_S 65 _t (the)_S 65 _t (case)_S 66 _t (in)_S 65 _t (which)_S 65 _t (the)_S 65 _t (single)_S 66 _t (or)_S 65 _t (double)_S gsave 0 0 translate 4 4 scale 100 _gs 100 _gs 846 1587 _m _sp 846 1587 844 1587 844 1551 846 1551 4 _pl _cp 100 _gs 852 1587 _m _sp 852 1587 850 1587 850 1551 852 1551 4 _pl _cp _f _s grestore gsave 0 0 translate 4 4 scale 100 _gs 100 _gs 907 1587 _m _sp 907 1587 905 1587 905 1551 907 1551 4 _pl _cp 100 _gs 913 1587 _m _sp 913 1587 911 1587 911 1551 913 1551 4 _pl _cp _f _s grestore gsave 0 0 translate 4 4 scale 100 _gs 100 _gs 1111 1587 _m _sp 1111 1587 1109 1587 1109 1551 1111 1551 4 _pl _cp 100 _gs 1117 1587 _m _sp 1117 1587 1115 1587 1115 1551 1117 1551 4 _pl _cp _f _s grestore gsave 0 0 translate 4 4 scale 100 _gs 100 _gs 1158 1587 _m _sp 1158 1587 1156 1587 1156 1551 1158 1551 4 _pl _cp 100 _gs 1164 1587 _m _sp 1164 1587 1162 1587 1162 1551 1164 1551 4 _pl _cp _f _s grestore 1200 6202 _m (dogleg)_S 94 _t (step)_S 94 _t (must)_S 93 _t (be)_S 94 _t (used,)_S 94 _t 3375 6202 _m 3413 6202 _m /Times-BoldR 550 _ff (s)_S /Times-RomanR 330 _ff 3484 6276 _m (CP)_S 3618 6276 _m /Times-RomanR 550 _ff 3618 6202 _m 3656 6202 _m /Times-RomanR 330 _ff 3656 6161 _m (2)_S 3711 6161 _m /Times-RomanR 550 _ff 3711 6202 _m 93 _t /Symbol 550 _ff (\243)_S /Times-RomanR 550 _ff 94 _t /Symbol 550 _ff (d)_S /Times-RomanR 330 _ff 4089 6161 _m (k)_S 4144 6161 _m /Times-RomanR 550 _ff 4144 6202 _m 94 _t /Symbol 550 _ff (\243)_S /Times-RomanR 550 _ff 94 _t 4433 6202 _m 4471 6202 _m /Times-BoldR 550 _ff (s)_S /Times-RomanR 330 _ff 4542 6276 _m (N)_S 4621 6276 _m /Times-RomanR 550 _ff 4621 6202 _m 4659 6202 _m /Times-RomanR 330 _ff 4659 6161 _m (2)_S 4714 6161 _m /Times-RomanR 550 _ff 4714 6202 _m (.)_S 187 _t (For)_S 94 _t (the)_S 93 _t (single)_S 94 _t (dogleg)_S 94 _t (case)_S 94 _t (the)_S 93 _t (new)_S 94 _t (point)_S 94 _t (is)_S 93 _t (at)_S 94 _t (the)_S 1200 6002 _m (intersection)_S 50 _t (of)_S 51 _t (the)_S 50 _t (line)_S 50 _t (from)_S 50 _t (the)_S 50 _t (Cauchy)_S 50 _t (point)_S 50 _t (to)_S 50 _t (the)_S 51 _t (Newton)_S 50 _t (step)_S 50 _t (with)_S 50 _t (the)_S 50 _t (border)_S 50 _t (of)_S 50 _t (the)_S 50 _t (trust)_S 50 _t (region.)_S 100 _t (The)_S 1200 5802 _m (double)_S 85 _t (dogleg)_S 86 _t (step)_S 85 _t (is)_S 86 _t (similar)_S 85 _t (except)_S 86 _t (that)_S 85 _t (only)_S 86 _t (a)_S 85 _t (fraction)_S 86 _t (of)_S 85 _t (the)_S 86 _t (Newton)_S 85 _t (step)_S 86 _t (is)_S 85 _t (used.)_S 171 _t (This)_S 85 _t (case)_S 86 _t (is)_S 1200 5602 _m (illustrated)_S 61 _t (in)_S 61 _t (Figure)_S 61 _t (2.)_S 122 _t 1620 5202 _m (The)_S 89 _t (variable)_S 89 _t (ETAFAC)_S 89 _t (controls)_S 89 _t (how)_S 89 _t (far)_S 89 _t (along)_S 89 _t (the)_S 89 _t (Newton)_S 90 _t (step)_S 89 _t (the)_S 89 _t (second)_S 89 _t (dogleg)_S 89 _t (is.)_S 178 _t (When)_S 1200 5002 _m (ETAFAC)_S 63 _t (is)_S 63 _t (1)_S 63 _t (the)_S 63 _t (single)_S 63 _t (dogleg)_S 63 _t (is)_S 63 _t (being)_S 63 _t (used.)_S 126 _t (As)_S 63 _t (it)_S 63 _t (approaches)_S 63 _t (0)_S 63 _t (the)_S 63 _t (more)_S 62 _t (influence)_S 63 _t (the)_S 63 _t (Newton)_S 63 _t (step)_S 1200 4802 _m (has)_S 54 _t (in)_S 55 _t (determining)_S 55 _t (the)_S 55 _t (trust)_S 55 _t (region)_S 55 _t (step.)_S 109 _t (The)_S 55 _t (default)_S 55 _t (value)_S 55 _t (0.2)_S 55 _t (was)_S 54 _t (suggested)_S 55 _t (by)_S 55 _t (Dennis)_S 55 _t (and)_S 55 _t (Mei)_S 55 _t (\(1979\))_S 1200 4602 _m (and)_S 71 _t (used)_S 72 _t (by)_S 71 _t (Dennis)_S 72 _t (and)_S 71 _t (Schnabel)_S 72 _t (\(1983\).)_S 143 _t (Note)_S 72 _t (that)_S 71 _t (an)_S 72 _t (ETAFAC)_S 71 _t (of)_S 72 _t (zero)_S 71 _t (corresponds)_S 72 _t (to)_S 71 _t (a)_S 72 _t (minimum)_S 1200 4402 _m (fraction,)_S 61 _t /Symbol 550 _ff (g)_S /Times-BoldR 550 _ff (s)_S /Times-RomanR 330 _ff 2024 4476 _m (N)_S 2103 4476 _m /Times-RomanR 550 _ff 2103 4402 _m (,)_S 61 _t (of)_S 61 _t (the)_S 61 _t (Newton)_S 61 _t (step)_S 61 _t (being)_S 61 _t (used,)_S 61 _t (not)_S 61 _t (to)_S 61 _t (no)_S 61 _t (contribution.)_S 1620 4002 _m (Two)_S 52 _t (other)_S 51 _t (situations)_S 52 _t (can)_S 51 _t (occur.)_S 103 _t (If)_S 52 _t (the)_S 52 _t (Newton)_S 51 _t (step)_S 52 _t (is)_S 51 _t (within)_S 52 _t (the)_S 52 _t (trust)_S 51 _t (region)_S 52 _t (then)_S 51 _t (the)_S 52 _t (Newton)_S 51 _t (point)_S 1200 3802 _m (is)_S 57 _t (tested)_S 57 _t (and)_S 57 _t (the)_S 58 _t (trust)_S 57 _t (region)_S 57 _t (size)_S 57 _t (adjusted)_S 57 _t (immediately)_S 58 _t (to)_S 57 _t (the)_S 57 _t (length)_S 57 _t (of)_S 58 _t (the)_S 57 _t (Newton)_S 57 _t (step.)_S 114 _t (If)_S 57 _t (this)_S 57 _t (point)_S 58 _t (is)_S 1200 3602 _m (a)_S 60 _t (failure)_S 60 _t _U (no)_S _u 60 _t (line)_S 60 _t (search)_S 60 _t (is)_S 59 _t (conducted;)_S 60 _t (the)_S 60 _t (trust)_S 60 _t (region)_S 60 _t (is)_S 60 _t (decreased)_S 59 _t (and)_S 60 _t (a)_S 60 _t (new)_S 60 _t (point)_S 60 _t (found.)_S 119 _t (On)_S 60 _t (the)_S 59 _t (other)_S 1200 3402 _m (hand,)_S 51 _t (if)_S 50 _t (the)_S 50 _t (Cauchy)_S 50 _t (point)_S 51 _t (is)_S 50 _t (outside)_S 51 _t (the)_S 50 _t (trust)_S 50 _t (region,)_S 50 _t (then)_S 51 _t (the)_S 50 _t (intersection)_S 50 _t (of)_S 50 _t (the)_S 51 _t (steepest)_S 50 _t (descent)_S 50 _t (direction)_S 1200 3202 _m (and)_S 63 _t (the)_S 63 _t (trust)_S 63 _t (region)_S 63 _t (becomes)_S 63 _t (the)_S 64 _t (trial)_S 63 _t (point.)_S 126 _t (As)_S 63 _t (the)_S 63 _t (trust)_S 63 _t (region)_S 63 _t (size)_S 63 _t (decreases)_S 63 _t (this)_S 63 _t (final)_S 63 _t (situation)_S 63 _t (must)_S 1200 3002 _m (occur)_S 66 _t (thus)_S 67 _t (is)_S 66 _t (it)_S 66 _t (is)_S 66 _t (known)_S 66 _t (that)_S 66 _t (some)_S 67 _t (positive)_S 66 _t (step)_S 66 _t (in)_S 66 _t (the)_S 66 _t (steepest)_S 67 _t (descent)_S 66 _t (direction)_S 66 _t (can)_S 66 _t (always)_S 66 _t (be)_S 66 _t (found)_S 1200 2802 _m (which)_S 61 _t (produces)_S 61 _t (the)_S 61 _t (required)_S 61 _t (decrease)_S 61 _t (in)_S 61 _t (the)_S 61 _t (objective)_S 61 _t (function.)_S 1200 2602 _m 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 1200 1802 _m 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 61 _t 4886 1250 _m (-)_S 61 _t (22)_S 61 _t (-)_S _ep _bp /Times-RomanR 550 _ff 0 13200 10200 _ornt /_r { sflg {/_t {0 rmoveto}bdef /ron false def} { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse }bdef gsave 0 0 translate 4 4 scale _s 899 1104 723 2101 _cw _s 2 _w 1390 2451 _m 1390 2454 _l _s 1390 2454 _m 1390 2465 _l _s 1390 2465 _m 1389 2476 _l _s 1389 2476 _m 1388 2487 _l _s 1388 2487 _m 1387 2498 _l _s 1387 2498 _m 1385 2509 _l _s 1385 2509 _m 1383 2520 _l _s 1383 2520 _m 1380 2531 _l _s 1380 2531 _m 1377 2541 _l _s 1377 2541 _m 1374 2552 _l _s 1374 2552 _m 1370 2562 _l _s 1370 2562 _m 1366 2573 _l _s 1366 2573 _m 1362 2583 _l _s 1362 2583 _m 1357 2593 _l _s 1357 2593 _m 1352 2602 _l _s 1352 2602 _m 1347 2612 _l _s 1347 2612 _m 1341 2621 _l _s 1341 2621 _m 1335 2631 _l _s 1335 2631 _m 1328 2640 _l _s 1328 2640 _m 1322 2648 _l _s 1322 2648 _m 1314 2657 _l _s 1314 2657 _m 1307 2665 _l _s 1307 2665 _m 1299 2673 _l _s 1299 2673 _m 1292 2681 _l _s 1292 2681 _m 1284 2688 _l _s 1284 2688 _m 1275 2696 _l _s 1275 2696 _m 1266 2702 _l _s 1266 2702 _m 1258 2709 _l _s 1258 2709 _m 1248 2715 _l _s 1248 2715 _m 1239 2721 _l _s 1239 2721 _m 1230 2727 _l _s 1230 2727 _m 1220 2732 _l _s 1220 2732 _m 1210 2737 _l _s 1210 2737 _m 1200 2742 _l _s 1200 2742 _m 1190 2746 _l _s 1190 2746 _m 1179 2750 _l _s 1179 2750 _m 1169 2753 _l _s 1169 2753 _m 1158 2756 _l _s 1158 2756 _m 1147 2759 _l _s 1147 2759 _m 1137 2762 _l _s 1137 2762 _m 1126 2764 _l _s 1126 2764 _m 1115 2765 _l _s 1115 2765 _m 1104 2766 _l _s 1104 2766 _m 1093 2767 _l _s 1093 2767 _m 1082 2768 _l _s 1082 2768 _m 1071 2768 _l _s 1071 2768 _m _U 1060 2768 _l _s 1060 2768 _m _U 1049 2767 _l _s 1049 2767 _m 1038 2766 _l _s 1038 2766 _m 1027 2764 _l _s 1027 2764 _m 1016 2763 _l _s 1016 2763 _m 1005 2760 _l _s 1005 2760 _m 994 2758 _l _s 994 2758 _m 984 2755 _l _s 984 2755 _m 973 2752 _l _s 973 2752 _m 963 2748 _l _s 963 2748 _m 952 2744 _l _s 952 2744 _m 942 2739 _l _s 942 2739 _m 932 2735 _l _s 932 2735 _m 923 2730 _l _s 923 2730 _m 913 2724 _l _s 913 2724 _m 904 2718 _l _s 904 2718 _m 894 2712 _l _s 894 2712 _m 885 2706 _l _s 885 2706 _m 876 2699 _l _s 876 2699 _m 868 2692 _l _s 868 2692 _m 860 2685 _l _s 860 2685 _m 852 2677 _l _s 852 2677 _m 844 2669 _l _s 844 2669 _m 836 2661 _l _s 836 2661 _m 829 2653 _l _s 829 2653 _m 822 2644 _l _s 822 2644 _m 816 2635 _l _s 816 2635 _m 810 2626 _l _s 810 2626 _m 804 2617 _l _s 804 2617 _m 798 2607 _l _s 798 2607 _m 793 2598 _l _s 793 2598 _m 788 2588 _l _s 788 2588 _m 783 2578 _l _s 783 2578 _m 779 2567 _l _s 779 2567 _m 775 2557 _l _s 775 2557 _m 772 2547 _l _s 772 2547 _m 769 2536 _l _s 769 2536 _m 766 2525 _l _s 766 2525 _m 763 2515 _l _s 763 2515 _m 761 2504 _l _s 761 2504 _m 760 2493 _l _s 760 2493 _m 758 2482 _l _s 758 2482 _m 758 2471 _l _s 758 2471 _m 757 2460 _l _s 757 2460 _m 757 2449 _l _s 757 2449 _m 757 2438 _l _s 757 2438 _m 758 2427 _l _s 758 2427 _m 759 2416 _l _s 759 2416 _m 760 2405 _l _s 760 2405 _m 762 2394 _l _s 762 2394 _m 764 2383 _l _s 764 2383 _m 767 2372 _l _s 767 2372 _m 770 2362 _l _s 770 2362 _m 773 2351 _l _s 773 2351 _m 777 2341 _l _s 777 2341 _m 781 2330 _l _s 781 2330 _m 785 2320 _l _s 785 2320 _m 790 2310 _l _s 790 2310 _m 795 2300 _l _s 795 2300 _m 801 2291 _l _s 801 2291 _m 807 2281 _l _s 807 2281 _m 813 2272 _l _s 813 2272 _m 819 2263 _l _s 819 2263 _m 826 2255 _l _s 826 2255 _m 833 2246 _l _s 833 2246 _m 840 2238 _l _s 840 2238 _m 848 2230 _l _s 848 2230 _m 856 2222 _l _s 856 2222 _m 864 2214 _l _s 864 2214 _m 872 2207 _l _s 872 2207 _m 881 2200 _l _s 881 2200 _m 890 2194 _l _s 890 2194 _m 899 2188 _l _s 899 2188 _m 908 2182 _l _s 908 2182 _m 918 2176 _l _s 918 2176 _m 927 2171 _l _s 927 2171 _m 937 2166 _l _s 937 2166 _m 947 2161 _l _s 947 2161 _m 958 2157 _l _s 958 2157 _m 968 2153 _l _s 968 2153 _m 978 2150 _l _s 978 2150 _m 989 2147 _l _s 989 2147 _m 1000 2144 _l _s 1000 2144 _m 1011 2141 _l _s 1011 2141 _m 1021 2139 _l _s 1021 2139 _m 1032 2138 _l _s 1032 2138 _m 1043 2136 _l _s 1043 2136 _m 1054 2135 _l _s 1054 2135 _m 1065 2135 _l _s 1065 2135 _m 1076 2135 _l _s 1076 2135 _m 1087 2135 _l _s 1087 2135 _m 1098 2136 _l _s 1098 2136 _m 1110 2137 _l _s 1110 2137 _m 1120 2139 _l _s 1120 2139 _m 1131 2140 _l _s 1131 2140 _m 1142 2142 _l _s 1142 2142 _m 1153 2145 _l _s 1153 2145 _m 1164 2148 _l _s 1164 2148 _m 1174 2151 _l _s 1174 2151 _m 1184 2155 _l _s 1184 2155 _m 1195 2159 _l _s 1195 2159 _m 1205 2163 _l _s 1205 2163 _m 1215 2168 _l _s 1215 2168 _m 1225 2173 _l _s 1225 2173 _m 1234 2179 _l _s 1234 2179 _m 1244 2185 _l _s 1244 2185 _m 1253 2191 _l _s 1253 2191 _m 1262 2197 _l _s 1262 2197 _m 1271 2204 _l _s 1271 2204 _m 1279 2211 _l _s 1279 2211 _m 1288 2218 _l _s 1288 2218 _m 1296 2226 _l _s 1296 2226 _m 1303 2234 _l _s 1303 2234 _m 1311 2242 _l _s 1311 2242 _m 1318 2250 _l _s 1318 2250 _m 1325 2259 _l _s 1325 2259 _m 1331 2268 _l _s 1331 2268 _m 1338 2277 _l _s 1338 2277 _m 1344 2286 _l _s 1344 2286 _m 1349 2296 _l _s 1349 2296 _m 1355 2305 _l _s 1355 2305 _m 1359 2315 _l _s 1359 2315 _m 1364 2325 _l _s 1364 2325 _m 1368 2335 _l _s 1368 2335 _m 1372 2346 _l _s 1372 2346 _m 1376 2356 _l _s 1376 2356 _m 1379 2367 _l _s 1379 2367 _m 1382 2378 _l _s 1382 2378 _m 1384 2388 _l _s 1384 2388 _m 1386 2399 _l _s 1386 2399 _m 1388 2410 _l _s 1388 2410 _m 1389 2421 _l _s 1389 2421 _m 1390 2432 _l _s 1390 2432 _m 1390 2443 _l _s 1390 2443 _m 1390 2451 _l _s 1074 2451 _m 1518 2768 _l _s 1518 2769 _m 1785 2959 _l _s 1785 2956 _m 1518 2766 _l _s 1518 2771 _m 1785 2961 _l _s 1785 2955 _m 1518 2765 _l _s 1518 2768 _m 1785 2958 _l _s 1075 2451 _m 1119 2705 _l _s 1117 2705 _m 1072 2451 _l _s 1077 2451 _m 1121 2705 _l _s 1115 2705 _m 1071 2451 _l _s 1074 2451 _m 1118 2705 _l _s 1118 2706 _m 1518 2769 _l _s 1518 2766 _m 1118 2703 _l _s 1118 2707 _m 1518 2771 _l _s 1518 2765 _m 1118 2702 _l _s 1118 2705 _m 1518 2768 _l _s 1118 2705 _m 1162 2958 _l _s 1156 2953 _m 1156 2953 _l _s 1158 2955 _m 1158 2953 _l _s 1159 2953 _m 1159 2958 _l _s 1161 2960 _m 1161 2952 _l _s 1163 2952 _m 1163 2962 _l _s 1164 2960 _m 1164 2952 _l _s 1166 2951 _m 1166 2956 _l _s 1788 2958 _m 1791 2962 _l _s 1783 2961 _m 1783 2961 _l _s 1784 2962 _m 1784 2960 _l _s 1786 2959 _m 1786 2963 _l _s 1788 2963 _m 1788 2957 _l _s 1789 2956 _m 1789 2964 _l _s 1791 2965 _m 1791 2955 _l _s 1793 2957 _m 1793 2966 _l _s [36 18 ] 0 _d 1118 2705 _m 1785 2962 _l _s [] 0 _d 1065 2451 _m 766 2451 _l _s 1059 2446 _m 1059 2457 _l _s 1061 2456 _m 1061 2446 _l _s 1063 2447 _m 1063 2455 _l _s 1064 2455 _m 1064 2448 _l 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50 _t (chosen)_S 50 _t (at)_S 49 _t (the)_S 50 _t (first)_S 50 _t (intersection)_S 50 _t (with)_S 50 _t (the)_S 50 _t (trust)_S 49 _t (region)_S 50 _t (radius)_S 50 _t (of)_S 50 _t (a)_S 50 _t (line)_S 1800 7850 _m (drawn)_S 61 _t (from)_S 61 _t (the)_S 61 _t (current)_S 61 _t (point,)_S 61 _t /Times-BoldR 550 _ff (x)_S /Times-RomanR 330 _ff 4177 7809 _m (k)_S 4232 7809 _m /Times-RomanR 550 _ff 4232 7850 _m (,)_S 61 _t (to)_S 61 _t (the)_S 61 _t (Cauchy)_S 61 _t (point)_S 61 _t (then)_S 60 _t (to)_S 61 _t (a)_S 61 _t (point)_S 61 _t (in)_S 61 _t (the)_S 61 _t (direction)_S 60 _t (of)_S gsave 0 0 translate 4 4 scale 100 _gs 3 _w 100 _gs 1311 1949 _m _sp 1311 1949 1309 1949 1309 1913 1311 1913 4 _pl _cp 100 _gs 1317 1949 _m _sp 1317 1949 1315 1949 1315 1913 1317 1913 4 _pl _cp _f _s grestore gsave 0 0 translate 4 4 scale 100 _gs 100 _gs 1359 1949 _m _sp 1359 1949 1357 1949 1357 1913 1359 1913 4 _pl _cp 100 _gs 1365 1949 _m _sp 1365 1949 1363 1949 1363 1913 1365 1913 4 _pl _cp _f _s grestore 1800 7650 _m (the)_S 69 _t (Newton)_S 69 _t (step)_S 69 _t (at)_S 69 _t (a)_S 69 _t (distance)_S 69 _t (greater)_S 69 _t (than)_S 69 _t /Symbol 550 _ff (g)_S /Times-RomanR 550 _ff 69 _t 5235 7650 _m 5273 7650 _m /Times-BoldR 550 _ff (s)_S /Times-RomanR 330 _ff 5344 7724 _m (N)_S 5424 7724 _m /Times-RomanR 550 _ff 5424 7650 _m 5461 7650 _m /Times-RomanR 330 _ff 5461 7609 _m (2)_S 5516 7609 _m /Times-RomanR 550 _ff 5516 7650 _m 69 _t (and)_S 69 _t (finally)_S 69 _t (to)_S 69 _t (the)_S 69 _t (end)_S 69 _t (of)_S 69 _t (the)_S 69 _t (Newton)_S 1800 7450 _m (step.)_S 113 _t (If)_S 56 _t (the)_S 57 _t (Newton)_S 56 _t (step)_S 57 _t (is)_S 56 _t (within)_S 57 _t (the)_S 56 _t (trust)_S 57 _t (region)_S 56 _t (radius)_S 57 _t (then)_S 56 _t /Times-BoldR 550 _ff (x)_S /Times-RomanR 330 _ff 6562 7409 _m (k+1)_S 6734 7450 _m 6734 7525 _m (N)_S 6813 7525 _m /Times-RomanR 550 _ff 6813 7450 _m 57 _t (is)_S 56 _t (chosen)_S 57 _t (as)_S 56 _t (the)_S 57 _t (trial)_S 1800 7250 _m (point.)_S 113 _t (As)_S 56 _t (the)_S 57 _t (trust)_S 56 _t (region)_S 56 _t (shrinks,)_S 57 _t (the)_S 56 _t (Cauchy)_S 57 _t (point)_S 56 _t (must)_S 57 _t (eventually)_S 56 _t (be)_S 56 _t (outside)_S 57 _t (the)_S 56 _t (trust)_S 1800 7050 _m (region)_S 61 _t (so)_S 61 _t (successive)_S 61 _t (points)_S 61 _t (in)_S 61 _t (the)_S 61 _t (steepest)_S 61 _t (descent)_S 61 _t (direction)_S 61 _t (are)_S 61 _t (tried.)_S 61 _t 1620 6650 _m (The)_S 49 _t (most)_S 49 _t (complicated)_S 50 _t (feature)_S 49 _t (of)_S 49 _t (trust)_S 49 _t (region)_S 49 _t (methods)_S 50 _t (is)_S 49 _t (updating)_S 49 _t /Symbol 550 _ff (d)_S /Times-RomanR 550 _ff (.)_S 98 _t (In)_S 49 _t (NNES)_S 50 _t (updating)_S 49 _t (is)_S 49 _t (governed)_S 1200 6450 _m (by)_S 60 _t (the)_S 60 _t (objective)_S 60 _t (function,)_S 60 _t /Times-ItalicR 550 _ff (f)_S /Times-RomanR 550 _ff (,)_S 60 _t (even)_S 59 _t (if)_S 60 _t (the)_S 60 _t (step)_S 60 _t (is)_S 60 _t (accepted)_S 60 _t (by)_S 59 _t (the)_S 60 _t (step)_S 60 _t (size)_S 60 _t (criterion.)_S 120 _t (If)_S 60 _t (the)_S 60 _t (first)_S 59 _t (trial)_S 60 _t (point)_S 1200 6250 _m (is)_S 61 _t (an)_S 61 _t (improvement)_S 60 _t (over)_S 61 _t (the)_S 61 _t (previous,)_S 61 _t (is)_S 61 _t (not)_S 60 _t (the)_S 61 _t (Newton)_S 61 _t (point)_S 61 _t (and)_S 60 _t (there)_S 61 _t (is)_S 61 _t (close)_S 61 _t (agreement)_S 60 _t (between)_S 61 _t (the)_S 1200 6050 _m (model)_S 48 _t (and)_S 48 _t (the)_S 48 _t (objective)_S 48 _t (function)_S 48 _t (then)_S 48 _t (the)_S 48 _t (trust)_S 48 _t (region)_S 48 _t (size)_S 48 _t (is)_S 48 _t (increased)_S 48 _t (and)_S 48 _t (a)_S 48 _t (new)_S 48 _t (trial)_S 47 _t (point)_S 48 _t (tested.)_S 96 _t (There)_S 1200 5850 _m (are)_S 41 _t (two)_S 40 _t (methods,)_S 41 _t (selected)_S 41 _t (via)_S 40 _t (TRUPDM,)_S 41 _t (to)_S 41 _t (accomplish)_S 40 _t (this:)_S 41 _t (Powell's)_S 41 _t (\(1970\))_S 40 _t (method)_S 41 _t (and)_S 41 _t (modified)_S 40 _t (version)_S 1200 5650 _m (that)_S 61 _t (of)_S 61 _t (Dennis)_S 62 _t (and)_S 61 _t (Schnabel)_S 62 _t (\(1983\).)_S 122 _t (Usually)_S 62 _t /Symbol 550 _ff (d)_S /Times-RomanR 550 _ff 61 _t (is)_S 62 _t (multiplied)_S 61 _t (DELFAC)_S 62 _t (\(default)_S 61 _t (2\))_S 61 _t (if)_S 62 _t (agreement)_S 61 _t (is)_S 62 _t (good)_S 1200 5450 _m (but)_S 57 _t (NNES)_S 57 _t (uses)_S 58 _t (a)_S 57 _t (much)_S 57 _t (more)_S 57 _t (aggressive)_S 58 _t (approach)_S 57 _t (if)_S 57 _t (a)_S 57 _t (nonmontonic)_S 58 _t (search)_S 57 _t (is)_S 57 _t (being)_S 57 _t (conducted.)_S 115 _t (When)_S 57 _t /Symbol 550 _ff (d)_S /Times-RomanR 550 _ff 1200 5250 _m (is)_S 54 _t (increased)_S 54 _t (it)_S 55 _t (is)_S 54 _t (taken)_S 55 _t (to)_S 54 _t (the)_S 54 _t (maximum)_S 55 _t (length)_S 54 _t (possible,)_S 54 _t (the)_S 55 _t (length)_S 54 _t (of)_S 55 _t (the)_S 54 _t (Newton)_S 54 _t (step.)_S 109 _t (If)_S 55 _t (this)_S 54 _t (point)_S 55 _t (fails)_S 1200 5050 _m (the)_S 61 _t (trust)_S 61 _t (region)_S 61 _t (size)_S 61 _t (works)_S 61 _t (back)_S 61 _t (down)_S 61 _t (to)_S 61 _t (a)_S 61 _t (length)_S 61 _t (no)_S 61 _t (less)_S 61 _t (than)_S 61 _t (that)_S 61 _t (of)_S 61 _t (the)_S 61 _t (original)_S 61 _t (acceptable)_S 61 _t (step.)_S 122 _t 1620 4850 _m (If)_S 51 _t (the)_S 52 _t (original)_S 51 _t (trial)_S 51 _t (point)_S 52 _t (is)_S 51 _t (a)_S 51 _t (success,)_S 52 _t (but)_S 51 _t (not)_S 52 _t (an)_S 51 _t (improvement)_S 51 _t (over)_S 52 _t (the)_S 51 _t (previous)_S 51 _t (f,)_S 52 _t (then)_S 51 _t /Symbol 550 _ff (d)_S /Times-RomanR 550 _ff 51 _t (is)_S 52 _t (reduced)_S 1200 4650 _m (by)_S 58 _t (DELFAC.)_S 59 _t (If)_S 58 _t (it)_S 59 _t (is)_S 58 _t (a)_S 58 _t (failure)_S 59 _t (then)_S 58 _t (there)_S 59 _t (are)_S 58 _t (two)_S 58 _t (options)_S 59 _t (similar)_S 58 _t (to)_S 58 _t (those)_S 59 _t (for)_S 58 _t (line)_S 59 _t (searches,)_S 58 _t (controlled)_S 58 _t (by)_S 1200 4450 _m (GEOMS:)_S 89 _t (reduce)_S 88 _t /Symbol 550 _ff (d)_S /Times-RomanR 550 _ff 89 _t (by)_S 89 _t (a)_S 88 _t (factor)_S 89 _t (of)_S 89 _t (DELFAC,)_S 88 _t (or)_S 89 _t (minimizing)_S 89 _t (a)_S 88 _t (quadratic,)_S 89 _t (with)_S 89 _t (the)_S 89 _t (restriction)_S 88 _t /Symbol 550 _ff (d)_S /Times-RomanR 330 _ff 8597 4409 _m (new)_S 8781 4409 _m /Times-RomanR 550 _ff 8781 4450 _m 89 _t /Symbol 550 _ff (\316)_S /Times-RomanR 550 _ff 1200 4250 _m ([0.1)_S /Symbol 550 _ff (d)_S /Times-RomanR 330 _ff 1581 4209 _m (old)_S 1721 4209 _m /Times-RomanR 550 _ff 1721 4250 _m (,0.5)_S /Symbol 550 _ff (d)_S /Times-RomanR 330 _ff 2087 4209 _m (old)_S 2227 4209 _m /Times-RomanR 550 _ff 2227 4250 _m (].)_S 122 _t (NNES)_S 61 _t (stops)_S 61 _t (automatically)_S 61 _t (if)_S 61 _t (the)_S 61 _t (step)_S 61 _t (length)_S 61 _t (becomes)_S 61 _t (too)_S 61 _t (small,)_S 61 _t (i.e.,)_S 1200 2770 _m /Times-BoldR 550 _ff (3.4)_S 122 _t (Other)_S 61 _t (Features)_S /Times-RomanR 550 _ff gsave 0 0 translate 4 4 scale _s 163 1899 325 812 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale 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16 _ieq FE3F 1440 830 8 _ieq E1 904 829 8 _ieq C7 1096 829 16 _ieq FE3F 1440 829 8 _ieq E3 904 828 8 _ieq C3 1096 828 16 _ieq FC7F 1440 828 8 _ieq E3 904 827 8 _ieq E3 1096 827 16 _ieq FC5F 1440 827 8 _ieq C3 904 826 8 _ieq F3 1096 826 16 _ieq FC5F 1440 826 8 _ieq C7 904 825 8 _ieq F1 1096 825 16 _ieq FC1F 1440 825 8 _ieq C7 904 824 8 _ieq F9 1096 824 16 _ieq FC3F 1440 824 8 _ieq 8F 904 823 8 _ieq F9 1096 823 16 _ieq FE7F 1440 823 8 _ieq 9F 904 822 8 _ieq FC 1440 822 8 _ieq 3F 904 821 8 _ieq FC 1440 821 8 _ieq 3F 904 820 16 _ieq FE7F 1432 820 16 _ieq FE7F 912 819 8 _ieq 3F 1432 819 16 _ieq FE7F 912 818 8 _ieq 9F 1432 818 8 _ieq FC 912 817 8 _ieq 9F 1432 817 8 _ieq F9 912 816 8 _ieq CF 1432 816 8 _ieq F3 _s grestore 8595 3568 _m /Times-BoldR 550 _ff (\(25\))_S /Times-RomanR 550 _ff 1620 2370 _m /Times-BoldR 550 _ff (3.4.1)_S 122 _t (Lower)_S 61 _t (and)_S 61 _t (Upper)_S 61 _t (Bounds)_S /Times-RomanR 550 _ff 1620 1970 _m (Lower)_S 58 _t (and)_S 57 _t (upper)_S 58 _t (bounds)_S 57 _t (are)_S 58 _t (used)_S 57 _t (to)_S 58 _t (impose)_S 57 _t (two)_S 58 _t (types)_S 58 _t (of)_S 57 _t (constraints:)_S 58 _t (absolute)_S 57 _t (for)_S 58 _t (variables)_S 57 _t (which)_S 1200 1770 _m (must)_S 56 _t (stay)_S 57 _t (within)_S 57 _t (a)_S 56 _t (region)_S 57 _t (for)_S 57 _t (mathematical)_S 56 _t (reasons)_S 57 _t (such)_S 56 _t (as)_S 57 _t (logarithms)_S 57 _t (and)_S 56 _t (square)_S 57 _t (roots)_S 56 _t (and)_S 57 _t (physical)_S 57 _t (for)_S 4886 1250 _m (-)_S 61 _t (23)_S 61 _t (-)_S _ep _bp /Times-RomanR 550 _ff 0 13200 10200 _ornt /_r { sflg {/_t {0 rmoveto}bdef /ron false def} { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse }bdef 1200 11850 _m (those)_S 41 _t (which)_S 40 _t (represent)_S 41 _t (physical)_S 41 _t (quantities)_S 41 _t (which)_S 40 _t (have)_S 41 _t (meaning)_S 41 _t (only)_S 40 _t (in)_S 41 _t (certain)_S 41 _t (regions)_S 40 _t (such)_S 41 _t (as)_S 41 _t (mole)_S 41 _t (fraction)_S 1200 11650 _m (and)_S 56 _t (temperature.)_S 112 _t (These)_S 56 _t (are)_S 56 _t (handled)_S 56 _t (the)_S 56 _t (exactly)_S 56 _t (same)_S 56 _t (way)_S 56 _t (in)_S 56 _t (NNES.)_S 112 _t (The)_S 56 _t (distinction)_S 56 _t (is)_S 56 _t (made)_S 56 _t (because)_S 56 _t (it)_S 1200 11450 _m (may)_S 62 _t (not)_S 61 _t (be)_S 62 _t (necessary)_S 61 _t (constrain)_S 61 _t (physical)_S 62 _t (variables.)_S 123 _t (By)_S 61 _t (allowing)_S 61 _t (them)_S 62 _t (to)_S 61 _t (trespass)_S 62 _t (into)_S 61 _t (restricted)_S 61 _t (regions)_S 1200 11250 _m (the)_S 63 _t (solution)_S 63 _t (may)_S 63 _t (be)_S 63 _t (found)_S 63 _t (more)_S 63 _t (quickly.)_S 126 _t (Constraints)_S 63 _t (are)_S 63 _t (handled)_S 63 _t (in)_S 63 _t (a)_S 63 _t (similar)_S 63 _t (way)_S 63 _t (for)_S 63 _t (both)_S 63 _t (line)_S 64 _t (search)_S 1200 11050 _m (and)_S 77 _t (trust)_S 78 _t (region)_S 77 _t (methods.)_S 154 _t (The)_S 77 _t (procedure)_S 77 _t (is)_S 77 _t (different)_S 77 _t (from)_S 77 _t (that)_S 77 _t (described)_S 77 _t (for)_S 77 _t (the)_S 77 _t (Absolute)_S 77 _t (Newton's)_S 1200 10850 _m (method.)_S 122 _t 1620 10450 _m (Consider)_S 58 _t (the)_S 57 _t (line)_S 57 _t (search)_S 57 _t (case)_S 58 _t (where)_S 57 _t (the)_S 57 _t (first)_S 57 _t (trial)_S 58 _t (point)_S 57 _t (is)_S 57 _t (the)_S 58 _t (full)_S 57 _t (Newton)_S 57 _t (step.)_S 115 _t (When)_S 57 _t (a)_S 57 _t (constraint)_S 1200 10250 _m (is)_S 76 _t (violated)_S 76 _t (the)_S 75 _t (first)_S 76 _t (response)_S 76 _t (is)_S 76 _t (to)_S 75 _t (bring)_S 76 _t (the)_S 76 _t (violating)_S 75 _t (components)_S 76 _t (back)_S 76 _t (into)_S 75 _t (the)_S 76 _t (feasible)_S 76 _t (region)_S 75 _t (while)_S 1200 10050 _m (leaving)_S 52 _t (the)_S 52 _t (nonviolating)_S 52 _t (components)_S 52 _t (alone)_S 52 _t (thus)_S 52 _t (departing)_S 52 _t (from)_S 52 _t (the)_S 51 _t (Newton)_S 52 _t (direction.)_S 104 _t (For)_S 52 _t (each)_S 52 _t (violating)_S 1200 9850 _m (component)_S 62 _t (the)_S 62 _t (ratio)_S 62 _t (of)_S 63 _t (the)_S 62 _t (distance)_S 62 _t (from)_S 62 _t (the)_S 62 _t (trial)_S 62 _t (point)_S 63 _t (to)_S 62 _t (its)_S 62 _t (boundary)_S 62 _t (to)_S 62 _t (the)_S 62 _t (length)_S 63 _t (of)_S 62 _t (that)_S 62 _t (component)_S 1200 9650 _m (of)_S 52 _t (the)_S 52 _t (Newton)_S 53 _t (step)_S 52 _t (\(called)_S 53 _t (RATIO\))_S 52 _t (is)_S 52 _t (found.)_S 105 _t (Instead)_S 52 _t (of)_S 53 _t (projecting)_S 52 _t (onto)_S 52 _t (the)_S 52 _t (boundary)_S 53 _t (or)_S 52 _t (reflecting)_S 52 _t (in)_S 53 _t (the)_S 1200 9450 _m (boundary,)_S 61 _t (the)_S 61 _t (violators)_S 61 _t (are)_S 61 _t (taken)_S 61 _t (only)_S 61 _t (the)_S 61 _t (fraction)_S 61 _t (CONFAC)_S 61 _t (\(default)_S 61 _t (0.95\))_S 62 _t (of)_S 61 _t (the)_S 61 _t (way)_S 61 _t (from)_S 61 _t (the)_S 61 _t (current)_S 1200 9250 _m (point)_S 71 _t (to)_S 71 _t (the)_S 71 _t (boundary)_S 71 _t (if)_S 71 _t (RATIO)_S 70 _t /Symbol 550 _ff (\243)_S /Times-RomanR 550 _ff 71 _t (0.5)_S 71 _t (or)_S 71 _t (\(1/2\)CONFAC)_S 71 _t (of)_S 71 _t (the)_S 71 _t (way)_S 71 _t (if)_S 71 _t (RATIO)_S 71 _t (>)_S 71 _t (0.5.)_S 71 _t (as)_S 71 _t (illustrated)_S 71 _t (in)_S 1200 9050 _m (Figure)_S 59 _t (3.)_S 119 _t (This)_S 59 _t (creates)_S 59 _t (a)_S 59 _t (buffer)_S 59 _t (zone)_S 59 _t (near)_S 59 _t (the)_S 59 _t (constraints)_S 59 _t (aimed)_S 59 _t (at)_S 60 _t (reducing)_S 59 _t (the)_S 59 _t (chances)_S 59 _t (of)_S 59 _t (getting)_S 59 _t (stuck)_S 1200 8850 _m (at)_S 61 _t (a)_S 61 _t (constraint.)_S 61 _t gsave 0 0 translate 4 4 scale _s 899 915 817 1301 _cw _s 2 _w 845 1405 _m 1575 1405 _l _s 1571 1401 _m 1571 1410 _l _s 1572 1409 _m 1572 1401 _l _s 1573 1402 _m 1573 1409 _l _s 1575 1408 _m 1575 1403 _l _s 1576 1404 _m 1576 1407 _l _s 1578 1406 _m 1578 1404 _l _s 1579 1405 _m 1579 1406 _l _s 1210 1405 _m _U 1210 2096 _l _s 1205 2092 _m 1205 2092 _l _s 1207 2094 _m 1207 2092 _l _s 1208 2092 _m 1208 2097 _l _s 1209 2099 _m 1209 2092 _l _s 1211 2092 _m 1211 2099 _l _s 1212 2097 _m 1212 2092 _l _s 1214 2092 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1702 1568 _l _s 1702 1568 _m _U 1701 1568 _l _s 1701 1568 _m _U 1700 1569 _l _s 1700 1569 _m 1700 1569 _l _s 1700 1569 _m 1700 1570 _l _s 1700 1570 _m 1700 1588 _l _s 1697 1583 _m 1697 1583 _l _s 1697 1583 _m 1704 1583 _l _s 1459 1596 _m 1459 1599 _l _s 1459 1599 _m 1460 1602 _l _s 1460 1602 _m 1460 1593 _l _s 1460 1593 _m 1462 1592 _l _s 1462 1592 _m 1462 1604 _l _s 1462 1604 _m 1463 1605 _l _s 1463 1605 _m 1463 1591 _l _s 1463 1591 _m 1464 1590 _l _s 1464 1590 _m 1464 1605 _l _s 1464 1605 _m 1466 1606 _l _s 1466 1606 _m 1466 1590 _l _s 1466 1590 _m 1467 1590 _l _s 1467 1590 _m 1467 1606 _l _s 1467 1606 _m 1468 1606 _l _s 1468 1606 _m 1468 1590 _l _s 1468 1590 _m 1470 1590 _l _s 1470 1590 _m 1470 1605 _l _s 1470 1605 _m 1471 1605 _l _s 1471 1605 _m 1471 1591 _l _s 1471 1591 _m 1473 1592 _l _s 1473 1592 _m 1473 1604 _l _s 1473 1604 _m 1474 1602 _l _s 1474 1602 _m 1474 1593 _l _s 3300 2550 674 801 _cw _s grestore 2613 4850 _m (Figure)_S 61 _t (3)_S 122 _t (Handling)_S 61 _t (Constraints)_S 61 _t (When)_S 61 _t (RATIO)_S 61 _t (is)_S 61 _t (Greater)_S 61 _t (Than)_S 61 _t (0.5)_S 4203 4650 _m (RATIO)_S 61 _t (=)_S 61 _t (d1/\(d1)_S 61 _t (+)_S 61 _t (d2\))_S 61 _t 2220 4250 _m (In)_S 47 _t (the)_S 48 _t (above)_S 48 _t (example)_S 47 _t (component)_S 48 _t (x)_S /Times-RomanR 330 _ff 4800 4209 _m (1)_S 4855 4209 _m /Times-RomanR 550 _ff 4855 4250 _m 48 _t (violates)_S 47 _t (a)_S 48 _t (lower)_S 47 _t (bound.)_S 96 _t (The)_S 47 _t (ratio)_S 96 _t (d1/\(d1)_S 47 _t (+)_S 48 _t (d2\))_S 1800 4050 _m (is)_S 55 _t (less)_S 55 _t (than)_S 56 _t (the)_S 55 _t (cutoff,)_S 55 _t (0.5,)_S 55 _t (so)_S 55 _t (the)_S 55 _t (modified)_S 56 _t (point,)_S 55 _t /HelveticaR 600 _ff (A)_S /Times-RomanR 550 _ff (,)_S 55 _t (is)_S 55 _t (set.)_S 110 _t (The)_S 55 _t (directional)_S 55 _t (derivative)_S 55 _t (to)_S /HelveticaR 600 _ff 1800 3850 _m (A)_S /Times-RomanR 600 _ff 74 _t (is)_S 74 _t (checked.)_S 148 _t (If)_S 74 _t (it)_S 74 _t (is)_S 74 _t (positive)_S 74 _t (then)_S /HelveticaR 600 _ff 74 _t (A)_S /Times-RomanR 550 _ff 67 _t (is)_S 67 _t (disregarded)_S 68 _t (and)_S 67 _t (a)_S 67 _t (line)_S 68 _t (search)_S 67 _t (begins)_S 67 _t (at)_S /HelveticaR 600 _ff 74 _t (B)_S /Times-RomanR 600 _ff (.)_S 1800 3650 _m (Otherwise)_S /HelveticaR 600 _ff 52 _t (A)_S /Times-RomanR 550 _ff 48 _t (is)_S 48 _t (checked)_S 47 _t (first)_S 48 _t (and)_S 47 _t (if)_S 48 _t (it)_S 48 _t (is)_S 47 _t (not)_S 48 _t (acceptable)_S 48 _t (then,)_S 47 _t (again,)_S 48 _t (the)_S 48 _t (line)_S 47 _t (search)_S 48 _t (begins)_S 1800 3450 _m (at)_S /HelveticaR 600 _ff 55 _t (B)_S /Times-RomanR 550 _ff (.)_S 100 _t (Notice)_S 50 _t (that)_S /HelveticaR 600 _ff 54 _t (A)_S /Times-RomanR 550 _ff 50 _t (and)_S /HelveticaR 600 _ff 55 _t (B)_S /Times-RomanR 550 _ff 50 _t (are)_S 50 _t (not)_S 50 _t (on)_S 49 _t (the)_S 50 _t (boundary;)_S 50 _t (for)_S 50 _t (component)_S 50 _t (x)_S /Times-RomanR 330 _ff 6899 3409 _m (1)_S 6954 3409 _m /Times-RomanR 550 _ff 6954 3450 _m (,)_S 50 _t (they)_S 49 _t (are)_S 50 _t (only)_S 50 _t (95%)_S 1800 3250 _m (of)_S 61 _t (the)_S 61 _t (distance)_S 61 _t (from)_S 61 _t (the)_S 61 _t (current)_S 61 _t (point)_S 61 _t (to)_S 61 _t (the)_S 61 _t (first)_S 61 _t (violated)_S 61 _t (constraint.)_S 1620 2850 _m /Times-BoldR 550 _ff (3.4.2)_S 122 _t (Scaling)_S /Times-RomanR 550 _ff 1620 2450 _m (Scaling)_S 59 _t (can)_S 58 _t (be)_S 59 _t (used)_S 59 _t (for)_S 58 _t (both)_S 59 _t (the)_S 58 _t (variables)_S 59 _t (and)_S 58 _t (the)_S 59 _t (functions.)_S 117 _t (For)_S 58 _t (variable)_S 59 _t (scaling,)_S 58 _t (the)_S 59 _t (objective)_S 58 _t (is)_S 1200 2250 _m (to)_S 72 _t (make)_S 72 _t (the)_S 72 _t (solution)_S 72 _t (have)_S 73 _t (components)_S 72 _t (of)_S 72 _t (comparable)_S 72 _t (magnitude.)_S 144 _t (The)_S 73 _t (best)_S 72 _t (way)_S 72 _t (to)_S 72 _t (do)_S 72 _t (this)_S 72 _t (is)_S 72 _t (to)_S 72 _t (have)_S 1200 2050 _m (reasonably)_S 61 _t (scaled)_S 61 _t (equations)_S 61 _t (but)_S 61 _t (it)_S 61 _t (can)_S 61 _t (also)_S 61 _t (be)_S 61 _t (done)_S 61 _t (internally)_S 61 _t (via)_S 62 _t (the)_S 61 _t (vector)_S 61 _t (SCALEX)_S 61 _t (which)_S 61 _t (represents)_S 1200 1850 _m (a)_S 100 _t (diagonal)_S 101 _t (scaling)_S 101 _t (matrix.)_S 201 _t (Consider)_S 101 _t (a)_S 100 _t (simple)_S 101 _t (case)_S 101 _t (in)_S 101 _t (which)_S 101 _t (the)_S 100 _t (units)_S 101 _t (for)_S 101 _t (x)_S /Times-RomanR 330 _ff 7391 1809 _m (1)_S 7446 1809 _m /Times-RomanR 550 _ff 7446 1850 _m 100 _t (are)_S 101 _t (seconds)_S 101 _t (where)_S 4886 1250 _m (-)_S 61 _t (24)_S 61 _t (-)_S _ep _bp /Times-RomanR 550 _ff 0 13200 10200 _ornt /_r { sflg {/_t {0 rmoveto}bdef /ron false def} { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse }bdef 1200 11850 _m (milliseconds)_S 46 _t (would)_S 46 _t (be)_S 46 _t (more)_S 46 _t (appropriate)_S 46 _t (and)_S 46 _t (the)_S 46 _t (units)_S 46 _t (for)_S 45 _t (x)_S /Times-RomanR 330 _ff 5534 11809 _m (2)_S 5589 11809 _m /Times-RomanR 550 _ff 5589 11850 _m 46 _t (are)_S 46 _t (millimeters)_S 46 _t (where)_S 46 _t (meters)_S 46 _t (would)_S 46 _t (be)_S 45 _t (better.)_S 1200 11650 _m (In)_S 61 _t (this)_S 61 _t (case)_S 61 _t (the)_S 61 _t (scaling)_S 61 _t (matrix)_S 61 _t (would)_S 61 _t (be:)_S 1620 10370 _m (Variable)_S 81 _t (scaling)_S 81 _t (does)_S 82 _t (not)_S 81 _t (change)_S 81 _t (the)_S 82 _t (Newton)_S 81 _t (step)_S 81 _t (but)_S 82 _t (it)_S 81 _t (affects)_S 81 _t (the)_S 81 _t (trust)_S 82 _t (region)_S 81 _t (step)_S 82 _t (since)_S 81 _t (the)_S gsave 0 0 translate 4 4 scale _s 3 _w 163 1899 325 2712 _cw _s 3300 2550 674 801 _cw _s grestore gsave 0 0 translate 4 4 scale 1392 2865 16 _ieq E007 1576 2865 16 _ieq 801F 1392 2864 16 _ieq E007 1576 2864 16 _ieq 801F 1392 2863 16 _ieq E007 1576 2863 16 _ieq 801F 1392 2862 8 _ieq E3 1584 2862 8 _ieq 1F 1392 2861 8 _ieq E3 1584 2861 8 _ieq 1F 1392 2860 8 _ieq E3 1584 2860 8 _ieq 1F 1392 2859 8 _ieq E3 1584 2859 8 _ieq 1F 1392 2858 8 _ieq E3 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(setting)_S 65 _t (BYPASS)_S 65 _t (to)_S 65 _t (TRUE.)_S 130 _t (The)_S 65 _t (resulting)_S 65 _t (Newton)_S 65 _t (step)_S 65 _t (may)_S 1200 9754 _m (not)_S 56 _t (be)_S 57 _t (accurate)_S 56 _t (but)_S 56 _t (may)_S 57 _t (be)_S 56 _t (better)_S 56 _t (than)_S 56 _t (that)_S 57 _t (found)_S 56 _t (by)_S 56 _t (the)_S 56 _t (remedial)_S 57 _t (action.)_S 112 _t (In)_S 57 _t (cases)_S 56 _t (where)_S 56 _t (ill-conditioned)_S 1200 9554 _m (Jacobians)_S 61 _t (are)_S 61 _t (encountered)_S 61 _t (setting)_S 61 _t (scaling)_S 61 _t (factors)_S 61 _t (should)_S 61 _t (be)_S 61 _t (considered)_S 61 _t (to)_S 61 _t (reduce)_S 61 _t (the)_S 61 _t (condition)_S 61 _t (number.)_S 1620 9154 _m /Times-BoldR 550 _ff (3.4.6)_S 122 _t (Overflow)_S 61 _t (Checking)_S 61 _t (using)_S 61 _t (OVERCH)_S /Times-RomanR 550 _ff 1620 8754 _m (Switching)_S 46 _t (OVERCH)_S 45 _t (to)_S 46 _t (TRUE)_S 46 _t (forces)_S 45 _t (checking)_S 46 _t (at)_S 45 _t (some)_S 46 _t (key)_S 45 _t (locations)_S 46 _t (for)_S 46 _t (potential)_S 45 _t (overflows.)_S 92 _t (If)_S 45 _t (one)_S 1200 8554 _m (is)_S 109 _t (detected)_S 108 _t (\01510)_S /Times-RomanR 330 _ff 2437 8629 _m (MAXEXP)_S 2901 8629 _m /Times-RomanR 550 _ff 2901 8554 _m 108 _t (is)_S 108 _t (substituted)_S 108 _t (where)_S 108 _t (appropriate)_S 108 _t (and)_S 109 _t (a)_S 108 _t (warning)_S 108 _t (issued.)_S 216 _t (This)_S 108 _t (slows)_S 108 _t (down)_S 1200 8354 _m (computation)_S 65 _t (somewhat)_S 65 _t (and)_S 64 _t (is)_S 65 _t (intended)_S 65 _t (to)_S 65 _t (save)_S 64 _t (those)_S 65 _t (problems)_S 65 _t (which)_S 65 _t (would)_S 64 _t (overflow)_S 65 _t (only)_S 65 _t (slightly.)_S 129 _t (If)_S 1200 8154 _m (divergence)_S 61 _t (has)_S 61 _t (set)_S 61 _t (in)_S 61 _t (this)_S 61 _t (procedure)_S 61 _t (will)_S 61 _t (only)_S 61 _t (delay)_S 61 _t (the)_S 61 _t (inevitable.)_S 4886 1250 _m (-)_S 61 _t (27)_S 61 _t (-)_S _ep _bp /Times-RomanR 550 _ff 0 13200 10200 _ornt /_r { sflg {/_t {0 rmoveto}bdef /ron false def} { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse }bdef 4673 11850 _m /Times-BoldR 550 _ff (References)_S /Times-RomanR 550 _ff 1200 11250 _m (1.)_S 1606 11250 _m (Abaffy,)_S 61 _t (J.)_S 61 _t (and)_S 61 _t (Spedicato,)_S 61 _t (E.;)_S 61 _t /Times-ItalicR 550 _ff (ABS)_S 61 _t (Projection)_S 61 _t (Algorithms)_S /Times-RomanR 550 _ff (;)_S 61 _t (Wiley,)_S 61 _t (New)_S 61 _t (York,)_S 61 _t (NY)_S 61 _t (\(1989\))_S 1200 11050 _m (2.)_S 1606 11050 _m (Allgower,)_S 59 _t (E.L.)_S 59 _t (and)_S 58 _t (Georg,)_S 59 _t (K.;)_S 59 _t /Times-ItalicR 550 _ff (Numerical)_S 59 _t (Continuation)_S 59 _t (Methods)_S /Times-RomanR 550 _ff (;)_S 58 _t (Springer-Verlag,)_S 59 _t (New)_S 59 _t (York,)_S 59 _t (NY)_S 1606 10850 _m (\(1990\))_S 1200 10650 _m (3.)_S 1606 10650 _m (Armijo,)_S 44 _t (L.;)_S 44 _t ("Minimization)_S 44 _t (of)_S 44 _t (functions)_S 45 _t (having)_S 44 _t (Lipschitz-continuous)_S 44 _t (first)_S 44 _t (partial)_S 44 _t (derivatives";)_S /Times-ItalicR 550 _ff 44 _t (Pacific)_S 1606 10450 _m (J.)_S 61 _t (Math.,)_S 61 _t /Times-BoldR 550 _ff (16)_S /Times-RomanR 550 _ff (,)_S 61 _t (1-3)_S 61 _t (\(1966\))_S 1200 10250 _m (4.)_S 1606 10250 _m (Broyden,)_S 59 _t (C.)_S 60 _t (G.;)_S 60 _t ("A)_S 60 _t (class)_S 59 _t (of)_S 60 _t (methods)_S 60 _t (for)_S 60 _t (solving)_S 60 _t (nonlinear)_S 59 _t (simultaneous)_S 60 _t (equations";)_S 60 _t /Times-ItalicR 550 _ff (Math.)_S 60 _t (Comp.)_S /Times-RomanR 550 _ff (,)_S 1606 10050 _m /Times-BoldR 550 _ff (19)_S /Times-RomanR 550 _ff (,)_S 61 _t (577-593)_S 61 _t (\(1965\))_S 1200 9850 _m (5.)_S 1606 9850 _m (Dennis,)_S 84 _t (J.)_S 83 _t (E.)_S 84 _t (and)_S 84 _t (Mei,)_S 84 _t (H.)_S 83 _t (H.)_S 84 _t (W.;)_S 84 _t ("Two)_S 84 _t (new)_S 84 _t (unconstrained)_S 83 _t (optimization)_S 84 _t (algorithms)_S 84 _t (which)_S 84 _t (use)_S 1606 9650 _m (function)_S 61 _t (and)_S 61 _t (gradient)_S 61 _t (values";)_S 61 _t /Times-ItalicR 550 _ff (J.)_S 61 _t (Optim.)_S 61 _t (Theory)_S 61 _t (Appl.)_S /Times-RomanR 550 _ff (,)_S 61 _t /Times-BoldR 550 _ff (28)_S /Times-RomanR 550 _ff (,)_S 61 _t (453-482)_S 61 _t (\(1979\))_S 1200 9450 _m (6.)_S 1606 9450 _m (Dennis,)_S 103 _t (J.)_S 104 _t (E.)_S 103 _t (and)_S 104 _t (Schnabel,)_S 103 _t (R.)_S 104 _t (B.;)_S 103 _t /Times-ItalicR 550 _ff (Numerical)_S 104 _t (Methods)_S 103 _t (for)_S 104 _t (Unconstrained)_S 103 _t (Optimization)_S 104 _t (and)_S 1606 9250 _m (Nonlinear)_S 61 _t (Equations)_S /Times-RomanR 550 _ff (;)_S 61 _t (Prentice-Hall,)_S 61 _t (Englewood)_S 61 _t (Cliffs,)_S 61 _t (NJ)_S 61 _t (\(1983\))_S 1200 9050 _m (7.)_S 1606 9050 _m (Deuflhard,)_S 54 _t (P.;)_S 53 _t ("A)_S 54 _t (modified)_S 54 _t (Newton)_S 53 _t (Method)_S 54 _t (for)_S 54 _t (the)_S 54 _t (solution)_S 54 _t (of)_S 53 _t (ill-conditioned)_S 54 _t (systems)_S 54 _t (of)_S 54 _t (nonlinear)_S 1606 8850 _m (equations)_S 61 _t (with)_S 61 _t (applications)_S 61 _t (to)_S 61 _t (multiple)_S 61 _t (shooting";)_S 61 _t /Times-ItalicR 550 _ff (Numer.)_S 61 _t (Math.)_S /Times-RomanR 550 _ff (,)_S 61 _t /Times-BoldR 550 _ff (22)_S /Times-RomanR 550 _ff (,)_S 61 _t (289-315)_S 61 _t (\(1974\))_S 1200 8650 _m (8.)_S 1606 8650 _m (Deuflhard,)_S 54 _t (P.;)_S 55 _t ("A)_S 54 _t (relaxation)_S 54 _t (factor)_S 55 _t (for)_S 54 _t (the)_S 54 _t (modified)_S 55 _t (Newton)_S 54 _t (method";)_S 54 _t (in)_S 55 _t /Times-ItalicR 550 _ff (Optimization)_S 54 _t (and)_S 54 _t (Optimal)_S 1606 8450 _m (Control)_S /Times-RomanR 550 _ff (,)_S 62 _t (Bulirsch,)_S 63 _t (R.,)_S 62 _t (Oettli,)_S 63 _t (W.)_S 62 _t (and)_S 63 _t (Stoer,)_S 62 _t (J.,)_S 63 _t (eds.,)_S 62 _t (Lecture)_S 62 _t (Notes)_S 63 _t (in)_S 62 _t (Math.,)_S 63 _t /Times-BoldR 550 _ff (472)_S /Times-RomanR 550 _ff (,)_S 62 _t (59-73,)_S 63 _t (Springer,)_S 1606 8250 _m (New)_S 61 _t (York,)_S 61 _t (NY)_S 61 _t (\(1975\))_S 1200 8050 _m (9.)_S 1606 8050 _m (Garcia,)_S 50 _t (C.B.)_S 50 _t (and)_S 50 _t (Zangwill,)_S 50 _t (W.I.;)_S 50 _t /Times-ItalicR 550 _ff (Pathways)_S 50 _t (to)_S 50 _t (Solutions,)_S 50 _t (Fixed)_S 50 _t (Points)_S 51 _t (and)_S 50 _t (Equilibria)_S /Times-RomanR 550 _ff (;)_S 50 _t (Prentice-Hall,)_S 1606 7850 _m (Englewood)_S 61 _t (Cliffs,)_S 61 _t (NJ)_S 61 _t (\(1981\))_S 1200 7650 _m (10.)_S 1606 7650 _m (Grippo,)_S 73 _t (L.,)_S 73 _t (Lampariello,)_S 73 _t (F.)_S 73 _t (and)_S 73 _t (Lucidi,)_S 73 _t (S.;)_S 73 _t ("A)_S 73 _t (nonmonotone)_S 73 _t (line)_S 73 _t (search)_S 73 _t (technique)_S 73 _t (for)_S 73 _t (Newton's)_S 1606 7450 _m (method";)_S 61 _t /Times-ItalicR 550 _ff (SIAM)_S 61 _t (J.)_S 61 _t (Numer.)_S 61 _t (Anal.)_S /Times-RomanR 550 _ff (,)_S 61 _t /Times-BoldR 550 _ff (23)_S /Times-RomanR 550 _ff (,)_S 61 _t (707-716)_S 61 _t (\(1986\))_S 1200 7250 _m (11.)_S 1606 7250 _m (Hiebert,)_S 69 _t (K.)_S 69 _t (L.;)_S 69 _t ("A)_S 69 _t (comparison)_S 68 _t (of)_S 69 _t (software)_S 69 _t (which)_S 69 _t (solves)_S 69 _t (systems)_S 69 _t (of)_S 69 _t (nonlinear)_S 68 _t (equations";)_S 69 _t /Times-ItalicR 550 _ff (Sandia)_S 1606 7050 _m (Tech.)_S 61 _t (Rep.)_S 61 _t (SAND)_S /Times-RomanR 550 _ff (80-0181,)_S 61 _t (Sandia)_S 61 _t (National)_S 61 _t (Laboratories,)_S 61 _t (Albequerque,)_S 61 _t (New)_S 61 _t (Mexico)_S 61 _t (\(1980\))_S 1200 6850 _m (12.)_S 1606 6850 _m (Kearfott,)_S 58 _t (R.B.)_S 58 _t (and)_S 59 _t (Novoa)_S 58 _t (III,)_S 58 _t (M.;)_S 58 _t ("Algorithm)_S 59 _t (681)_S 58 _t (INTBIS,)_S 58 _t (a)_S 58 _t (portable)_S 58 _t (interval)_S 59 _t (Newton)_S 174 _t (/bisection)_S 1606 6650 _m (package";)_S 61 _t /Times-ItalicR 550 _ff (ACM)_S 61 _t (Trans.)_S 61 _t (Math.)_S 61 _t (Soft.)_S /Times-RomanR 550 _ff (,)_S 61 _t /Times-BoldR 550 _ff (16)_S /Times-RomanR 550 _ff (,)_S 61 _t (152-157)_S 1200 6450 _m (13.)_S 1606 6450 _m (Lee,)_S 69 _t (J.)_S 70 _t (and)_S 69 _t (Lee,)_S 70 _t (W.)_S 69 _t (K.;)_S 70 _t ("Least)_S 69 _t (squares)_S 69 _t (updates)_S 70 _t (for)_S 69 _t (quasi-Newton)_S 70 _t (methods)_S 69 _t (in)_S 70 _t (process)_S 69 _t (design)_S 70 _t (and)_S 1606 6250 _m (simulation";)_S 61 _t /Times-ItalicR 550 _ff (Comp.)_S 61 _t (Chem.)_S 61 _t (Eng.)_S /Times-RomanR 550 _ff (,)_S 61 _t /Times-BoldR 550 _ff (13)_S /Times-RomanR 550 _ff (,)_S 61 _t (717-723)_S 61 _t (\(1989\))_S 1200 6050 _m (14.)_S 1606 6050 _m (Neumaier,)_S 55 _t (A.;)_S 55 _t /Times-ItalicR 550 _ff (Interval)_S 55 _t (Methods)_S 55 _t (for)_S 56 _t (Systems)_S 55 _t (of)_S 55 _t (Equations)_S /Times-RomanR 550 _ff (;)_S 55 _t (Cambridge)_S 55 _t (University)_S 55 _t (Press,)_S 55 _t (New)_S 56 _t (York,)_S 1606 5850 _m (NY)_S 61 _t (\(1990\))_S 1200 5650 _m (15.)_S 1606 5650 _m (Ortega,)_S 42 _t (J.M.)_S 42 _t (and)_S 41 _t (Rheinboldt,)_S 42 _t (W.C.;)_S 41 _t /Times-ItalicR 550 _ff (Iterative)_S 42 _t (Solutions)_S 41 _t (for)_S 42 _t (Nonlinear)_S 41 _t (Equations)_S 42 _t (in)_S 42 _t (Several)_S 41 _t (Variables)_S /Times-RomanR 550 _ff (;)_S 1606 5450 _m (Academic)_S 61 _t (Press,)_S 61 _t (New)_S 61 _t (York,)_S 61 _t (NY)_S 61 _t (\(1970\))_S 1200 5250 _m (16.)_S 1606 5250 _m (Powell,)_S 59 _t (M.)_S 59 _t (J.)_S 59 _t (D.;)_S 59 _t ("A)_S 59 _t (FORTRAN)_S 59 _t (subroutine)_S 59 _t (for)_S 59 _t (solving)_S 59 _t (systems)_S 59 _t (of)_S 59 _t (nonlinear)_S 59 _t (algebraic)_S 59 _t (equations";)_S 1606 5050 _m (in)_S 55 _t /Times-ItalicR 550 _ff (Numerical)_S 54 _t (Methods)_S 55 _t (for)_S 55 _t (Nonlinear)_S 55 _t (Equations)_S /Times-RomanR 550 _ff (,)_S 55 _t (Rabinowitz,)_S 55 _t (P.,)_S 54 _t (ed.,)_S 55 _t (Gordon)_S 55 _t ()_S 55 _t (Breach,)_S 55 _t (New)_S 55 _t (York,)_S 1606 4850 _m (NY)_S 61 _t (\(1970\))_S 1200 4650 _m (17.)_S 1606 4650 _m (Shacham,)_S 69 _t (M.;)_S 70 _t ("Recent)_S 70 _t (developments)_S 69 _t (in)_S 70 _t (solution)_S 70 _t (techniques)_S 70 _t (for)_S 69 _t (systems)_S 70 _t (of)_S 70 _t (non-linear)_S 70 _t (equations";)_S 1606 4450 _m (Paper)_S 54 _t (presented)_S 54 _t (at)_S 53 _t (the)_S 54 _t (second)_S 53 _t (International)_S 54 _t (Conference)_S 53 _t (on)_S 54 _t (Foundations)_S 53 _t (of)_S 54 _t (Computer)_S 53 _t (Aided)_S 54 _t (Process)_S 1606 4250 _m (Design,)_S 61 _t (Snowmass,)_S 61 _t (CO,)_S 61 _t (19-24)_S 61 _t (June)_S 61 _t (\(1983\))_S 1200 4050 _m (18.)_S 1606 4050 _m (Shacham,)_S 78 _t (M.;)_S 79 _t ("Numerical)_S 78 _t (solution)_S 79 _t (of)_S 79 _t (constrained)_S 78 _t (nonlinear)_S 79 _t (algebraic)_S 78 _t (equations";)_S 79 _t /Times-ItalicR 550 _ff (Inter.)_S 78 _t (J.)_S 79 _t (Num.)_S 1606 3850 _m (Methods)_S 61 _t (in)_S 61 _t (Eng.)_S /Times-RomanR 550 _ff (,)_S 61 _t /Times-BoldR 550 _ff (23)_S /Times-RomanR 550 _ff (,)_S 61 _t (1455-1481)_S 61 _t (\(1986\))_S 4886 1250 _m (-)_S 61 _t (28)_S 61 _t (-)_S _ep _bp /Times-RomanR 550 _ff 0 13200 10200 _ornt /_r { sflg {/_t {0 rmoveto}bdef /ron false def} { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse }bdef 1606 11850 _m /Times-BoldR 550 _ff (Appendix)_S 61 _t (1)_S 122 _t (Generic)_S 61 _t (Driver)_S /Times-RomanR 550 _ff /CourierR 500 _ff 1200 11450 _m 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(********************************************************************)_S 1200 6250 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (EXTERNAL)_S 100 _t (FCN,JACOB)_S 1200 6050 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (COMMON/NNES_1/MATSUP)_S 1200 5850 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (COMMON/NNES_2/WRNSUP)_S 1200 5650 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (COMMON/NNES_3/BYPASS)_S 1200 5450 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (COMMON/NNES_4/NFETOT)_S 1200 5250 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (OPEN\(UNIT=NUNIT,FILE='NNESDR.OUT',STATUS='UNKNOWN'\))_S 1200 5050 _m (********************************************************************)_S 1200 4850 _m (*)_S 6600 _t (*)_S 1200 4650 _m (*)_S 700 _t (INSERT)_S 100 _t (INITIAL)_S 100 _t (ESTIMATES)_S 3500 _t (*)_S 1200 4450 _m (*)_S 6600 _t (*)_S 1200 4250 _m (********************************************************************)_S 1200 4050 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (CALL)_S 100 _t (SETUP\(ABSNEW)_S 100 _t (,CAUCHY)_S 100 _t (,DEUFLH)_S 100 _t (,GEOMS)_S 200 _t (,LINESR)_S 100 _t (,)_S 1200 3850 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1300 _t (NEWTON)_S 100 _t (,OVERCH)_S 100 _t (,ACPTCR)_S 100 _t (,ITSCLF)_S 100 _t (,ITSCLX)_S 100 _t (,)_S 1200 3650 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1300 _t (JACTYP)_S 100 _t (,JUPDM)_S 200 _t (,MAXEXP)_S 100 _t (,MAXIT)_S 200 _t (,MAXNS)_S 200 _t (,)_S 1200 3450 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1300 _t (MAXQNS)_S 100 _t (,MINQNS)_S 100 _t (,N)_S 600 _t (,NARMIJ)_S 100 _t (,NINITN)_S 100 _t (,)_S 1200 3250 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1300 _t (NJACCH)_S 100 _t (,OUTPUT)_S 100 _t (,QNUPDM)_S 100 _t (,STOPCR)_S 100 _t (,SUPPRS)_S 100 _t (,)_S 1200 3050 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1300 _t (TRUPDM)_S 100 _t (,ALPHA)_S 200 _t (,CONFAC)_S 100 _t (,DELTA)_S 200 _t (,DELFAC)_S 100 _t (,)_S 1200 2850 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1300 _t (ETAFAC)_S 100 _t (,FDTOLJ)_S 100 _t (,FTOL)_S 300 _t (,LAM0)_S 300 _t (,MCHEPS)_S 100 _t (,)_S 1200 2650 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1300 _t (MSTPF)_S 200 _t (,NSTTOL)_S 100 _t (,OMEGA)_S 200 _t (,RATIOF)_S 100 _t (,SIGMA)_S 200 _t (,)_S 1200 2450 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1300 _t (STPTOL)_S 100 _t (,BOUNDL)_S 100 _t (,BOUNDU)_S 100 _t (,SCALEF)_S 100 _t (,SCALEX)_S 200 _t (,)_S 1200 2250 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1300 _t (HELP)_S 300 _t (\))_S 4886 1250 _m /Times-RomanR 550 _ff (-)_S 61 _t (29)_S 61 _t (-)_S /CourierR 500 _ff _ep _bp /CourierR 500 _ff 0 13200 10200 _ornt /_r { sflg {/_t {0 rmoveto}bdef /ron false def} { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse }bdef 1200 11850 _m (********************************************************************)_S 1200 11650 _m (*)_S 6600 _t (*)_S 1200 11450 _m (*)_S 700 _t (INSERT)_S 100 _t (CHANGES)_S 100 _t (TO)_S 100 _t (DEFAULT)_S 100 _t (SETTINGS)_S 2500 _t (*)_S 1200 11250 _m (*)_S 6600 _t (*)_S 1200 11050 _m (********************************************************************)_S 1606 10850 _m 100 _t 100 _t 100 _t 100 _t (CALL)_S 100 _t (NNES\(ABSNEW)_S 100 _t (,CAUCHY)_S 100 _t (,DEUFLH)_S 100 _t (,GEOMS)_S 200 _t (,LINESR)_S 100 _t (,)_S 1200 10650 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1200 _t (NEWTON)_S 100 _t (,OVERCH)_S 100 _t (,ACPTCR)_S 100 _t (,ITSCLF)_S 100 _t (,ITSCLX)_S 100 _t (,)_S 1200 10450 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1200 _t (JACTYP)_S 100 _t (,JUPDM)_S 200 _t (,MAXEXP)_S 100 _t (,MAXIT)_S 200 _t (,MAXNS)_S 200 _t (,)_S 1200 10250 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1200 _t (MAXQNS)_S 100 _t (,MGLL)_S 300 _t (,MINQNS)_S 100 _t (,N)_S 600 _t (,NARMIJ)_S 100 _t (,)_S 1200 10050 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1200 _t (NIEJEV)_S 100 _t (,NJACCH)_S 100 _t (,NJETOT)_S 100 _t (,NUNIT)_S 200 _t (,OUTPUT)_S 100 _t (,)_S 1200 9850 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1200 _t (QNUPDM)_S 100 _t (,STOPCR)_S 100 _t (,SUPPRS)_S 100 _t (,TRMCOD)_S 100 _t (,TRUPDM)_S 100 _t (,)_S 1200 9650 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1200 _t (ALPHA)_S 200 _t (,CONFAC)_S 100 _t (,DELTA)_S 200 _t (,DELFAC)_S 100 _t (,EPSMCH)_S 100 _t (,)_S 1200 9450 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1200 _t (ETAFAC)_S 100 _t (,FCNNEW)_S 100 _t (,FDTOLJ)_S 100 _t (,FTOL)_S 300 _t (,LAM0)_S 300 _t (,)_S 1200 9250 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1200 _t (MSTPF)_S 200 _t (,NSTTOL)_S 100 _t (,OMEGA)_S 200 _t (,RATIOF)_S 100 _t (,SIGMA)_S 200 _t (,)_S 1200 9050 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1200 _t (STPTOL)_S 100 _t (,A)_S 600 _t (,BOUNDL)_S 100 _t (,BOUNDU)_S 100 _t (,DELF)_S 300 _t (,)_S 1200 8850 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1200 _t (FSAVE)_S 200 _t (,FTRACK)_S 100 _t (,FVEC)_S 300 _t (,FVECC)_S 200 _t (,H)_S 600 _t (,)_S 1200 8650 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1200 _t (HHPI)_S 300 _t (,JAC)_S 400 _t (,PLEE)_S 300 _t (,RDIAG)_S 200 _t (,S)_S 600 _t (,)_S 1200 8450 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1200 _t (SBAR)_S 300 _t (,SCALEF)_S 100 _t (,SCALEX)_S 100 _t (,SN)_S 500 _t (,SSDHAT)_S 100 _t (,)_S 1200 8250 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1200 _t (STRACK)_S 100 _t (,VHAT)_S 300 _t (,WV1)_S 400 _t (,WV2)_S 400 _t (,WV3)_S 400 _t (,)_S 1200 8050 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1200 _t (WV4)_S 400 _t (,XC)_S 500 _t (,XPLUS)_S 200 _t (,XSAVE)_S 200 _t (,HELP)_S 300 _t (,)_S 1200 7850 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1200 _t (FCN)_S 400 _t (,JACOB)_S 200 _t (\))_S 1200 7650 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (STOP)_S 1200 7450 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (END)_S 1200 7050 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (SUBROUTINE)_S 100 _t (FCN\(OVERFL,N,FVEC,XC\))_S 1200 6850 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (IMPLICIT)_S 100 _t (DOUBLE)_S 100 _t (PRECISION)_S 100 _t (\(A-H,O-Z\))_S 1200 6650 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (DIMENSION)_S 100 _t (FVEC\(N\),XC\(N\))_S 1200 6450 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (COMMON/NNES_4/NFETOT)_S 1200 6250 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (LOGICAL)_S 100 _t (OVERFL)_S 1200 6050 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (OVERFL=.FALSE.)_S 1200 5850 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (NFETOT=NFETOT+1)_S 1200 5650 _m (********************************************************************)_S 1200 5450 _m (*)_S 6600 _t (*)_S 1200 5250 _m (*)_S 700 _t (INSERT)_S 100 _t (FUNCTIONS)_S 4300 _t (*)_S 1200 5050 _m (*)_S 6600 _t (*)_S 1200 4850 _m (********************************************************************)_S 1200 4650 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (RETURN)_S 1200 4450 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (END)_S 1200 4250 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (SUBROUTINE)_S 100 _t (JACOB\(OVERFL,N,JAC,XC\))_S 1200 4050 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (IMPLICIT)_S 100 _t (DOUBLE)_S 100 _t (PRECISION)_S 100 _t (\(A-H,O-Z\))_S 1200 3850 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (DOUBLE)_S 100 _t (PRECISION)_S 100 _t (JAC\(N,N\))_S 1200 3650 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (DIMENSION)_S 100 _t (XC\(N\))_S 100 _t 1200 3450 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (LOGICAL)_S 100 _t (OVERFL)_S 1200 3250 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (OVERFL=.FALSE.)_S 1200 3050 _m (********************************************************************)_S 1200 2850 _m (*)_S 6600 _t (*)_S 1200 2650 _m (*)_S 700 _t (INSERT)_S 100 _t (ANALYTICAL)_S 100 _t (JACOBIAN)_S 100 _t (IF)_S 100 _t (DESIRED)_S 2200 _t (*)_S 1200 2450 _m (*)_S 6600 _t (*)_S 1200 2250 _m (********************************************************************)_S 1200 2050 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (RETURN)_S 1200 1850 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (END)_S 4886 1250 _m /Times-RomanR 550 _ff (-)_S 61 _t (30)_S 61 _t (-)_S /CourierR 500 _ff _ep _bp /Times-RomanR 550 _ff 0 13200 10200 _ornt /_r { sflg {/_t {0 rmoveto}bdef /ron false def} { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse }bdef 1606 11850 _m /Times-BoldR 550 _ff (Appendix)_S 61 _t (2)_S 122 _t (Rosenbrock's)_S 61 _t (Banana)_S /Times-RomanR 550 _ff 1606 11450 _m (Calling)_S 61 _t (Program)_S /CourierR 500 _ff 1200 11050 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (PROGRAM)_S 100 _t (EX1)_S 1200 10850 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (IMPLICIT)_S 100 _t (DOUBLE)_S 100 _t (PRECISION)_S 100 _t (\(A-H,O-Z\))_S 1200 10650 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (PARAMETER)_S 100 _t (\()_S 200 _t (MGLL=)_S 500 _t (10,)_S 300 _t 1200 10450 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1500 _t (N=)_S 900 _t (2,)_S 1200 10250 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1500 _t (NUNIT=)_S 400 _t (10\))_S 1200 10050 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (DOUBLE)_S 100 _t (PRECISION)_S 500 _t 1200 9850 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1500 _t (JAC\(N,N\))_S 200 _t (,LAM0)_S 700 _t (,MCHEPS)_S 500 _t (,MSTPF)_S 400 _t (,)_S 1200 9650 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1500 _t (NSTTOL)_S 1000 _t 1200 9450 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (INTEGER)_S 600 _t (ACPTCR)_S 400 _t (,OUTPUT)_S 500 _t (,QNUPDM)_S 500 _t (,STOPCR)_S 300 _t (,)_S 1200 9250 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1500 _t (SUPPRS)_S 400 _t (,TRMCOD)_S 500 _t (,TRUPDM)_S 500 _t 1200 9050 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (DIMENSION)_S 400 _t (A\(N,N\))_S 400 _t (,BOUNDL\(N\))_S 200 _t (,BOUNDU\(N\))_S 200 _t (,DELF\(N\))_S 200 _t (,)_S 1200 8850 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1500 _t (FSAVE\(N\))_S 200 _t (,FTRACK\(0:MGLL-1\))_S 700 _t (,FVEC\(N\))_S 200 _t (,)_S 1200 8650 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1500 _t (FVECC\(N\))_S 200 _t (,H\(N,N\))_S 500 _t (,HHPI\(N\))_S 400 _t (,PLEE\(N,N\),)_S 1200 8450 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1500 _t (RDIAG\(N\))_S 200 _t (,S\(N\))_S 700 _t (,SBAR\(N\))_S 400 _t (,SCALEF\(N\),)_S 1200 8250 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1500 _t (SCALEX\(N\))_S 100 _t (,SN\(N\))_S 600 _t (,SSDHAT\(N\))_S 200 _t (,)_S 1200 8050 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1500 _t (STRACK\(0:MGLL-1\))_S 600 _t (,VHAT\(N\))_S 400 _t (,WV1\(N\))_S 300 _t (,)_S 1200 7850 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1500 _t (WV2\(N\))_S 400 _t (,WV3\(N\))_S 500 _t (,WV4\(N\))_S 500 _t (,XC\(N\))_S 400 _t (,)_S 1200 7650 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1500 _t (XPLUS\(N\))_S 200 _t (,XSAVE\(N\))_S 200 _t 1200 7450 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (LOGICAL)_S 600 _t (BYPASS)_S 400 _t (,CAUCHY)_S 500 _t (,DEUFLH)_S 500 _t (,GEOMS)_S 400 _t (,)_S 1200 7250 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1500 _t (LINESR)_S 400 _t (,MATSUP)_S 500 _t (,NEWTON)_S 500 _t (,OVERCH)_S 300 _t (,)_S 1200 7050 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1500 _t (WRNSUP)_S 1200 6850 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (EXTERNAL)_S 100 _t (FCN,JACOB)_S 1200 6650 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (COMMON/NNES_1/MATSUP)_S 1200 6450 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (COMMON/NNES_2/WRNSUP)_S 1200 6250 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (COMMON/NNES_3/BYPASS)_S 1200 6050 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (COMMON/NNES_4/NFETOT)_S 1200 5850 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (OPEN\(UNIT=NUNIT,FILE='ROSENB.OUT',STATUS='UNKNOWN'\))_S 1200 5650 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (XC\(1\)=-1.2D0)_S 1200 5450 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (XC\(2\)=1.0D0)_S 1200 5250 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (CALL)_S 100 _t (SETUP\(ABSNEW)_S 100 _t (,CAUCHY)_S 100 _t (,DEUFLH)_S 100 _t (,GEOMS)_S 200 _t (,LINESR)_S 100 _t (,)_S 1200 5050 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1300 _t (NEWTON)_S 100 _t (,OVERCH)_S 100 _t (,ACPTCR)_S 100 _t (,ITSCLF)_S 100 _t (,ITSCLX)_S 100 _t (,)_S 1200 4850 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1300 _t (JACTYP)_S 100 _t (,JUPDM)_S 200 _t (,MAXEXP)_S 100 _t (,MAXIT)_S 200 _t (,MAXNS)_S 200 _t (,)_S 1200 4650 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1300 _t (MAXQNS)_S 100 _t (,MINQNS)_S 100 _t (,N)_S 600 _t (,NARMIJ)_S 100 _t (,NINITN)_S 100 _t (,)_S 1200 4450 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1300 _t (NJACCH)_S 100 _t (,OUTPUT)_S 100 _t (,QNUPDM)_S 100 _t (,STOPCR)_S 100 _t (,SUPPRS)_S 100 _t (,)_S 1200 4250 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1300 _t (TRUPDM)_S 100 _t (,ALPHA)_S 200 _t (,CONFAC)_S 100 _t (,DELTA)_S 200 _t (,DELFAC)_S 100 _t (,)_S 1200 4050 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1300 _t (ETAFAC)_S 100 _t (,FDTOLJ)_S 100 _t (,FTOL)_S 300 _t (,LAM0)_S 300 _t (,MCHEPS)_S 100 _t (,)_S 1200 3850 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1300 _t (MSTPF)_S 200 _t (,NSTTOL)_S 100 _t (,OMEGA)_S 200 _t (,RATIOF)_S 100 _t (,SIGMA)_S 200 _t (,)_S 1200 3650 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1300 _t (STPTOL)_S 100 _t (,BOUNDL)_S 100 _t (,BOUNDU)_S 100 _t (,SCALEF)_S 100 _t (,SCALEX)_S 200 _t (,)_S 1200 3450 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1300 _t (HELP)_S 300 _t (\))_S 1606 3250 _m 100 _t 100 _t 100 _t 100 _t (CALL)_S 100 _t (NNES\(ABSNEW)_S 100 _t (,CAUCHY)_S 100 _t (,DEUFLH)_S 100 _t (,GEOMS)_S 200 _t (,LINESR)_S 100 _t (,)_S 1200 3050 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1200 _t (NEWTON)_S 100 _t (,OVERCH)_S 100 _t (,ACPTCR)_S 100 _t (,ITSCLF)_S 100 _t (,ITSCLX)_S 100 _t (,)_S 1200 2850 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1200 _t (JACTYP)_S 100 _t (,JUPDM)_S 200 _t (,MAXEXP)_S 100 _t (,MAXIT)_S 200 _t (,MAXNS)_S 200 _t (,)_S 1200 2650 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1200 _t (MAXQNS)_S 100 _t (,MGLL)_S 300 _t (,MINQNS)_S 100 _t (,N)_S 600 _t (,NARMIJ)_S 100 _t (,)_S 1200 2450 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1200 _t (NIEJEV)_S 100 _t (,NJACCH)_S 100 _t (,NJETOT)_S 100 _t (,NUNIT)_S 200 _t (,OUTPUT)_S 100 _t (,)_S 1200 2250 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1200 _t (QNUPDM)_S 100 _t (,STOPCR)_S 100 _t (,SUPPRS)_S 100 _t (,TRMCOD)_S 100 _t (,TRUPDM)_S 100 _t (,)_S 1200 2050 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1200 _t (ALPHA)_S 200 _t (,CONFAC)_S 100 _t (,DELTA)_S 200 _t (,DELFAC)_S 100 _t (,EPSMCH)_S 100 _t (,)_S 1200 1850 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1200 _t (ETAFAC)_S 100 _t (,FCNNEW)_S 100 _t (,FDTOLJ)_S 100 _t (,FTOL)_S 300 _t (,LAM0)_S 300 _t (,)_S 4886 1250 _m /Times-RomanR 550 _ff (-)_S 61 _t (31)_S 61 _t (-)_S /CourierR 500 _ff _ep _bp /CourierR 500 _ff 0 13200 10200 _ornt /_r { sflg {/_t {0 rmoveto}bdef /ron false def} { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse }bdef 1200 11850 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1200 _t (MSTPF)_S 200 _t (,NSTTOL)_S 100 _t (,OMEGA)_S 200 _t (,RATIOF)_S 100 _t (,SIGMA)_S 200 _t (,)_S 1200 11650 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1200 _t (STPTOL)_S 100 _t (,A)_S 600 _t (,BOUNDL)_S 100 _t (,BOUNDU)_S 100 _t (,DELF)_S 300 _t (,)_S 1200 11450 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1200 _t (FSAVE)_S 200 _t (,FTRACK)_S 100 _t (,FVEC)_S 300 _t (,FVECC)_S 200 _t (,H)_S 600 _t (,)_S 1200 11250 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1200 _t (HHPI)_S 300 _t (,JAC)_S 400 _t (,PLEE)_S 300 _t (,RDIAG)_S 200 _t (,S)_S 600 _t (,)_S 1200 11050 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1200 _t (SBAR)_S 300 _t (,SCALEF)_S 100 _t (,SCALEX)_S 100 _t (,SN)_S 500 _t (,SSDHAT)_S 100 _t (,)_S 1200 10850 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1200 _t (STRACK)_S 100 _t (,VHAT)_S 300 _t (,WV1)_S 400 _t (,WV2)_S 400 _t (,WV3)_S 400 _t (,)_S 1200 10650 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1200 _t (WV4)_S 400 _t (,XC)_S 500 _t (,XPLUS)_S 200 _t (,XSAVE)_S 200 _t (,HELP)_S 300 _t (,)_S 1200 10450 _m 100 _t 100 _t 100 _t 100 _t 100 _t ($)_S 1200 _t (FCN)_S 400 _t (,JACOB)_S 200 _t (\))_S 1200 10250 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (STOP)_S 1200 10050 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (END)_S 1200 9250 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (SUBROUTINE)_S 100 _t (FCN\(OVERFL,N,FVEC,XC\))_S 1200 9050 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (IMPLICIT)_S 100 _t (DOUBLE)_S 100 _t (PRECISION)_S 100 _t (\(A-H,O-Z\))_S 1200 8850 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (DIMENSION)_S 100 _t (FVEC\(N\),XC\(N\))_S 1200 8650 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (COMMON/NNES_4/NFETOT)_S 1200 8450 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (LOGICAL)_S 100 _t (OVERFL)_S 1200 8250 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (OVERFL=.FALSE.)_S 1200 8050 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (NFETOT=NFETOT+1)_S 1200 7850 _m (c)_S 1200 7650 _m (c)_S 700 _t (Rosenbrock)_S 100 _t (Banana)_S 100 _t (Function)_S 1200 7450 _m (c)_S 1200 7250 _m (c)_S 700 _t (f1)_S 100 _t (=)_S 100 _t (10\(x2)_S 100 _t (-)_S 100 _t (x1**2\))_S 1200 7050 _m (c)_S 700 _t (f2)_S 100 _t (=)_S 100 _t (1)_S 100 _t (-)_S 100 _t (x1)_S 1200 6850 _m (c)_S 1200 6650 _m (c)_S 700 _t (start:)_S 200 _t (\(-1.2,1\))_S 1200 6450 _m (c)_S 1200 6250 _m (c)_S 700 _t (sol'n:)_S 200 _t (\(1,1\))_S 1200 6050 _m (c)_S 1200 5850 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (FVEC\(1\)=10.0D0*\(XC\(2\)-XC\(1\)**2\))_S 1200 5650 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (FVEC\(2\)=1.0D0-XC\(1\))_S 1200 5450 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (RETURN)_S 1200 5250 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (END)_S 1200 5050 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (SUBROUTINE)_S 100 _t (JACOB\(OVERFL,N,JAC,XC\))_S 1200 4850 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (IMPLICIT)_S 100 _t (DOUBLE)_S 100 _t (PRECISION)_S 100 _t (\(A-H,O-Z\))_S 1200 4650 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (DOUBLE)_S 100 _t (PRECISION)_S 100 _t (JAC\(N,N\))_S 1200 4450 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (DIMENSION)_S 100 _t (XC\(N\))_S 100 _t 1200 4250 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (LOGICAL)_S 100 _t (OVERFL)_S 1200 4050 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (OVERFL=.FALSE.)_S 1200 3650 _m (The)_S 100 _t (analytical)_S 100 _t (jacobian)_S 100 _t (would)_S 100 _t (look)_S 100 _t (like)_S 1200 3250 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (JAC\(1,1\)=-20.0D0*XC\(1\))_S 1200 3050 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (JAC\(1,2\)=10.0D0)_S 1200 2850 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (JAC\(2,1\)=-1.0D0)_S 1200 2650 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (JAC\(2,2\)=0.0D0)_S 100 _t 1200 2250 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (RETURN)_S 1200 2050 _m 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t 100 _t (END)_S /Times-RomanR 550 _ff 4886 1250 _m (-)_S 61 _t (32)_S 61 _t (-)_S _ep _bp /Times-RomanR 550 _ff 0 13200 10200 _ornt /_r { sflg {/_t {0 rmoveto}bdef /ron false def} { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse }bdef 1606 11850 _m (Output)_S /CourierR 500 _ff 1200 11450 _m 100 _t 100 _t (************************************************************************)_S 1200 11250 _m 100 _t 100 _t (************************************************************************)_S 1200 11050 _m 100 _t 100 _t (************************************************************************)_S 1200 10850 _m 100 _t 100 _t (*)_S 7000 _t (*)_S 1200 10650 _m 100 _t 100 _t (*)_S 3300 _t (NNES)_S 3300 _t (*)_S 1200 10450 _m 100 _t 100 _t (*)_S 7000 _t (*)_S 1200 10250 _m 100 _t 100 _t (*)_S 900 _t (NONMONOTONIC)_S 100 _t (NONLINEAR)_S 100 _t (EQUATION)_S 100 _t (SOLVER)_S 200 _t (VERSION)_S 100 _t (1.05)_S 900 _t (*)_S 1200 10050 _m 100 _t 100 _t (*)_S 7000 _t (*)_S 1200 9850 _m 100 _t 100 _t (*)_S 2100 _t (COPYRIGHT)_S 100 _t (1991,)_S 100 _t (BY)_S 100 _t (R.S.)_S 100 _t (BAIN)_S 2100 _t (*)_S 1200 9650 _m 100 _t 100 _t (*)_S 7000 _t (*)_S 1200 9450 _m 100 _t 100 _t (************************************************************************)_S 1200 9250 _m 100 _t 100 _t (************************************************************************)_S 1200 9050 _m 100 _t 100 _t (************************************************************************)_S 1200 8050 _m 100 _t 100 _t (************************************************************************)_S 1200 7850 _m 100 _t 100 _t (************************************************************************)_S 1200 7650 _m 100 _t 100 _t (*)_S 7000 _t (*)_S 1200 7450 _m 100 _t 100 _t (*)_S 400 _t (INITIAL)_S 100 _t (ESTIMATES)_S 1600 _t (INITIAL)_S 100 _t (FUNCTION)_S 100 _t (VALUES)_S 1000 _t (*)_S 1200 7250 _m 100 _t 100 _t (*)_S 7000 _t (*)_S 1200 7050 _m 100 _t 100 _t (*)_S 200 _t (X\()_S 200 _t (1\))_S 100 _t (=)_S 300 _t (-1.200E+00)_S 1500 _t (F\()_S 200 _t (1\))_S 100 _t (=)_S 300 _t (-4.400E+00)_S 1100 _t (*)_S 1200 6850 _m 100 _t 100 _t (*)_S 200 _t (X\()_S 200 _t (2\))_S 100 _t (=)_S 400 _t (1.000E+00)_S 1500 _t (F\()_S 200 _t (2\))_S 100 _t (=)_S 400 _t (2.200E+00)_S 1100 _t (*)_S 1200 6650 _m 100 _t 100 _t (*)_S 7000 _t (*)_S 1200 6450 _m 100 _t 100 _t (*)_S 200 _t (INITIAL)_S 100 _t (OBJECTIVE)_S 100 _t (FUNCTION)_S 100 _t (VALUE)_S 100 _t (=)_S 200 _t (1.210E+01)_S 2300 _t (*)_S 1200 6250 _m 100 _t 100 _t (*)_S 7000 _t (*)_S 1200 6050 _m 100 _t 100 _t (************************************************************************)_S 1200 5450 _m 100 _t 100 _t (************************************************************************)_S 1200 5250 _m 100 _t 100 _t (*)_S 7000 _t (*)_S 1200 5050 _m 100 _t 100 _t (*)_S 600 _t (CONVERGENCE)_S 100 _t (REACHED;)_S 100 _t (TERMINATION)_S 100 _t (CODE:)_S 100 _t (...............)_S 500 _t (2)_S 400 _t (*)_S 1200 4850 _m 100 _t 100 _t (*)_S 7000 _t (*)_S 1200 4650 _m 100 _t 100 _t (*)_S 7000 _t (*)_S 1200 4450 _m 100 _t 100 _t (*)_S 1000 _t (FINAL)_S 100 _t (ESTIMATES)_S 1900 _t (FINAL)_S 100 _t (FUNCTION)_S 100 _t (VALUES)_S 500 _t (*)_S 1200 4250 _m 100 _t 100 _t (*)_S 7000 _t (*)_S 1200 4050 _m 100 _t 100 _t (*)_S 600 _t (X\()_S 200 _t (1\))_S 100 _t (=)_S 400 _t (1.00000E+00)_S 1400 _t (F\()_S 200 _t (1\))_S 100 _t (=)_S 400 _t (3.05532E-07)_S 400 _t (*)_S 1200 3850 _m 100 _t 100 _t (*)_S 600 _t (X\()_S 200 _t (2\))_S 100 _t (=)_S 400 _t (1.00000E+00)_S 1400 _t (F\()_S 200 _t (2\))_S 100 _t (=)_S 400 _t (1.11022E-16)_S 400 _t (*)_S 1200 3650 _m 100 _t 100 _t (*)_S 7000 _t (*)_S 1200 3450 _m 100 _t 100 _t (*)_S 600 _t (FINAL)_S 100 _t (OBJECTIVE)_S 100 _t (FUNCTION)_S 100 _t (VALUE:)_S 300 _t (4.667E-14)_S 2100 _t (*)_S 1200 3250 _m 100 _t 100 _t (*)_S 7000 _t (*)_S 1200 3050 _m 100 _t 100 _t (*)_S 7000 _t (*)_S 1200 2850 _m 100 _t 100 _t (*)_S 600 _t (TOTAL)_S 100 _t (NUMBER)_S 100 _t (OF)_S 100 _t (ITERATIONS:)_S 100 _t (..........................)_S 500 _t (2)_S 400 _t (*)_S 1200 2650 _m 100 _t 100 _t (*)_S 600 _t (TOTAL)_S 100 _t (NUMBER)_S 100 _t (OF)_S 100 _t (LINE)_S 100 _t (SEARCH)_S 100 _t (FUNCTION)_S 100 _t (EVALUATIONS:)_S 100 _t (....)_S 500 _t (3)_S 400 _t (*)_S 1200 2450 _m 100 _t 100 _t (*)_S 600 _t (TOTAL)_S 100 _t (NUMBER)_S 100 _t (OF)_S 100 _t (EXPLICIT)_S 100 _t (JACOBIAN)_S 100 _t (EVALUATIONS:)_S 100 _t (.......)_S 500 _t (2)_S 400 _t (*)_S 1200 2250 _m 100 _t 100 _t (*)_S 600 _t (TOTAL)_S 100 _t (NUMBER)_S 100 _t (OF)_S 100 _t (FUNCTION)_S 100 _t (EVALUATIONS:)_S 100 _t (................)_S 500 _t (7)_S 400 _t (*)_S 1200 2050 _m 100 _t 100 _t (*)_S 7000 _t (*)_S 1200 1850 _m 100 _t 100 _t (************************************************************************)_S /Times-RomanR 550 _ff 4886 1250 _m (-)_S 61 _t (33)_S 61 _t (-)_S _ep _ed end .