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\title{\bf  NUMERICAL ANALYSIS  \\
  MATHEMATICS OF SCIENTIFIC COMPUTING}
\smallskip
\author{ David Kincaid and Ward Cheney \\
        \copyright 1991 Brooks/Cole Publishing Co.\\
ISBN 0--534--13014--3}

\date{March 15, 1991}
\maketitle

\section*{Introduction}
The following table lists files containing sample programs 
based on the pseudocode given in the textbook cited above.
They are intended  primarily as a learning and teaching aid 
for use with this book.
We believe that these computer routines are coded in a clear and
easy-to-understand style.
We have
intentionally included few comment statements 
so that students will read the code and study the algorithms---they
can add comments as they decipher them.
These programs are usable on computer systems with Fortran 77 compilers, from
small personal computers to large scientific computing machines.
However, they do not contain all of the ``bells-and-whistles'' of
robust state-of-the-art software such as may be found in general-purpose
scientific libraries.
Nevertheless, they are adequate for many small nonpathological
problems.

\noindent
\section*{Installation and Usage}  On a Unix system, unpack the file
kincaid-cheney.shar as follows

\indent
{\tt sh kincaid-cheney.shar}

\noindent
These programs will run as is on any computer with a 
standard Fortran 77 compiler.  However, the statement
{\tt data epsi/1.0e-6/}
in some routines  should be changed to the
machine epsilon (single precision roundoff error) for the 
computer that is to be used.
Compile and execute the program on file romberg.f as follows

\indent
{\tt f77 romberg.f}

\indent
{\tt a.out}

\section*{Availability}

For information on the availability of this software, contact either
the publisher of the textbook or the authors at the following addresses.
\medskip
\begin{center}
\begin{tabular}{lcl}
Brooks/Cole Publishing Co.& &Center for Numerical Analysis\\
511 Forest Lodge Road& &University of Texas at Austin\\
Pacific Grove, CA 93950--5098& &Austin, TX 78713--8510\\[0.1in]
(408) 373--0728& &(512) 471--1242\\
fax: (408) 375--6414& &fax: (512) 471--9038 \\
&&kincaid@cs.utexas.edu
\end{tabular}
\end{center}

\newpage
\begin{center}
\begin{tabular}{lrl}
{\bf File Name} & {\bf Pages} & {\bf Description of Code\quad (Subprogram Names)} \\[0.1in]
{\bf \tt elimit.f} & 10 & Example of a slowly converging sequence \\
{\bf \tt sqrt2.f}  & 10 & Example of a rapidly converging sequence \\
{\bf \tt nest.f} & 14 & Nested multiplication \\[0.1in]
{\bf \tt epsi.f} & 36 & Approximate value of machine precision \\
{\bf \tt depsi.f} & 36 & Approximate value of double precision machine precision \\
{\bf \tt ex2s22.f} & 43--44 & Loss of significance \\
{\bf \tt unstab1.f} & 49 & Example of an unstable sequence \\
{\bf \tt unstab2.f} & 50 & Example of another unstable sequence \\
{\bf \tt instab.f} & 50 & Example of numerical instability  \\[0.1in]
{\bf \tt ex1s31.f} & 58--59 & Bisection method to find root of $\exp(x)=\sin x$ \quad({\bf bisect}) \\
{\bf \tt ex1s32.f} & 65 & Newton's method example \\
{\bf \tt ex2s32.f} & 68 & Simple Newton's method \\
{\bf \tt ex3s32.f} & 69--70 & Implicit function example \\
{\bf \tt ex1s33.f} & 76 & Secant method example \quad ({\bf f\,}) \\
{\bf \tt ex3s34.f} & 83--84 & Contractive mapping example \\
{\bf \tt ex3s35.f} & 93 & Horner's method example \\
{\bf \tt ex6s35.f} & 94 & Newton's method on a given polynomial \quad({\bf horner}) \\
{\bf \tt ex7s35.f} & 99 & Bairstow's method example \\
{\bf \tt laguerre.f} & 102 & Laguerre's method example \\[0.1in]
{\bf \tt forsub.f} & 127 & Forward substitution example \\
{\bf \tt bacsub.f} & 127 & Backward substitution example \\
{\bf \tt pforsub.f} & 128 & Forward substitution for a permuted system \\
{\bf \tt pbacsub.f} & 128 & Backward substitution for a permuted system \\
{\bf \tt genlu.f} & 130 & General LU-factorization example \\
{\bf \tt doolt.f} & 131 & Doolittle's-factorization example \\
{\bf \tt cholsky.f} & 134 & Cholesky-factorization example\\
{\bf \tt bgauss.f} & 143 & Basic Gaussian elimination \\
{\bf \tt pbgauss.f} & 145 & Basic Gaussian elimination with pivoting \\
{\bf \tt gauss.f} & 148 & Gaussian elimination with scaled row pivoting \\
{\bf \tt paxeb.f} & 150 & Solves $Lz=Pb$ and then $Ux=z$ \quad ({\bf gauss}) \\
{\bf \tt yaec.f} & 151 & Solves $U^{T}z=c$ and then $L^{T}Py=z$ \quad ({\bf gauss}) \\
{\bf \tt tri.f} & 155 & Tridiagonal system solver \quad ({\bf tri}) \\
{\bf \tt ex1s45.f} & 173 & Neumann series example \quad ({\bf setI, mult, store, add, prt}) \\
{\bf \tt ex2s45.f} & 175 & Gaussian elimination followed by iterative
improvement\\
&& \qquad ({\bf residual, gauss, solve}) \\
{\bf \tt ex1s46.f} & 182 & Example of Jacobi and Gauss-Seidel methods \\
{\bf \tt ex2s46.f} & 184 & Richardson method example (with scaling) \\
{\bf \tt jacobi.f} & 186 & Jacobi method example (with scaling) \\
{\bf \tt ex3s46.f} & 190 & Gauss-Seidel method (with scaling)\\
{\bf \tt ex6s46.f} & 200 & Chebyshev acceleration example \quad ({\bf extrap, cheb, vnorm}) \\
{\bf \tt steepd.f} & 207 & Steepest descent method example \quad ({\bf prod, mult}) \\
{\bf \tt cg.f} & 211 & Conjugate gradient method \quad ({\bf prod,
residual, mult}) \\
{\bf \tt pcg.f} & 217 & Jacobi preconditioned conjugate gradient method\\
& &  \qquad ({\bf prod, residual, mult}) 
\end{tabular}
\end{center}

\newpage
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\begin{tabular}{lrl}
{\bf File Name} & {\bf Pages} & {\bf Description of Code \quad (Subprogram
Names)} \quad (continued)\\[0.1in]
{\bf \tt ex1s51.f} & 231 & Power method example \quad ({\bf dot, prod, store, norm, normal}) \\
{\bf \tt poweracc.f} & 231 & Power method with Aitken acceleration\\
& &\qquad ({\bf dot, prod, store, norm, normal}) \\
{\bf \tt ex2s51.f} & 233 & Inverse power method example \\
& &\qquad ({\bf gauss, dot, prod, store, norm, normal, solve)} \\
{\bf \tt ipoweracc.f} & 233 & Inverse power method with Aitken
acceleration \\
& & \qquad ({\bf gauss, dot, prod, store, norm, normal, solve}) \\
{\bf \tt ex1s52.f} & 239 & Schur factorization example \quad ({\bf prtmtx, mult}) \\
{\bf \tt qrshif.f} & 248 & Modified Gram-Schmidt example \quad ({\bf prtmtx, mgs, mult}) \\
{\bf \tt ex1s53.f} & 253--255 & QR-factorization using Householder
transformations \\
	& &\qquad ({\bf  QRfac, setoI, prtmtx, UtimesA, findV, prod,}\\
	& &\qquad {\bf  formU, formW, trans, mult}) \\
{\bf \tt ex2s55.f} & 272--273 & QR-factorization example \\
	& &\qquad ({\bf QRfac, setoI, prtmtx, UtimesA, findV, prod, } \\
        & &\qquad {\bf formU, formW, trans, mult, copy, scale}) \\
{\bf \tt ex3s55.f} & 274 & Shifted QR-factorization example \\
& &\qquad ({\bf submtx, shiftA, unshiftA, hess, QRfac, setoI, }\\
& &\qquad {\bf  prtmtx, UtimesA, findU, findV,  prod, formU,  }\\
& &\qquad {\bf formW, Trans, mult, copy, scale}) \\[0.1in]
{\bf \tt coef.f} & 280--281 & Coefficients in the Newton form of a polynomial \\
{\bf \tt fft.f} & 419 & Fast Fourier transform example \quad ({\bf f\,}) \\
{\bf \tt adapta.f} & 426--428 & Adaptive approximation example \quad
({\bf f, max}) \\[0.1in]
{\bf \tt ex1s71.f} & 431--432 & Derivative approximations: forward difference formula \\
{\bf \tt ex2s71.f} & 434 & Derivative approximation: central difference \\
{\bf \tt ex5s71.f} & 437--438 & Derivative approximation: Richardson extrapolation \\
{\bf \tt ex6s71.f} & 440--441 & Richardson extrapolation \\
{\bf \tt gauss5.f} & 459 & Gaussian five-point quadrature example \\
{\bf \tt romberg.f} & 468 & Romberg extrapolation \\
{\bf \tt adapt.f} & 475 & Adaptive quadrature \\[0.1in]
{\bf \tt taylor.f} & 492 & Taylor-series method \\
{\bf \tt rk4.f} & 501--502 & Runge-Kutta method \quad ({\bf f, u}) \\
{\bf \tt rkfelberg.f} & 503--505 & Runge-Kutta-Fehlberg method \quad ({\bf f\,}) \\
{\bf \tt taysys.f} & 526--527 & Taylor series for systems \\[0.1in]
{\bf \tt exs91.f} & 576 & Boundary value problem (BVP): Explicit
method example\\
& & \qquad ({\bf a, b, vnorm}) \\
{\bf \tt exs92.f} & 582 &  BVP: Implicit method example \quad ({\bf tri, unorm}) \\
{\bf \tt exs93.f} & 589 & Finite difference method \quad ({\bf g\,}) \\
{\bf \tt ex3s96.f} & 613 & BVP: Method of characteristics \quad ({\bf f, g, df, tu}) \\
{\bf \tt mgrid1.f} & 624 & Multigrid method example \quad ({\bf vnorm}) \\
{\bf \tt exs98.f} & 625 & Damping of errors  \\
{\bf \tt mgrid2.f} & 630 & Multigrid method V-cycle \quad ({\bf vnorm}) \\[0.1in]
      
{\bf \tt code-info.tex}&&This \LaTeX\  file\\
{\bf \tt code-info.tty}&&This tty file
\end{tabular}
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