# LaTeX2HTML 0.6.4 (Tues Aug 30 1994)
# Associate image original text (scrambled) with physical files.
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$key = q/{}$kappa_2(A)=sigma_max(A)sigma_min(A)${}/;
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$key = q/{}$a_ii${}/;
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$key = q/{}$infty${}/;
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$key = q/{displaymath}A=ZTZ^H,{displaymath}/;
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$key = q/{}$3n^2${}/;
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$cached_env_img{$key} ='
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$key = q/{}$|hatx-x|_p${}/;
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$key = q/{displaymath}A=Qleft(arraycR0arrayright),quadmboxif$mgen$,{displaymath}/;
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$key = q/{displaymath}$n{displaymath}/;
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$key = q/{displaymath}y_1=0quadmboxandquady_2=T^-1_22d_2{displaymath}/;
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$key = q/{}$beta_m+1=cdots=beta_r=1${}/;
$cached_env_img{$key} ='
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$key = q/{displaymath}omega_infty=frac|r|_infty|A|_inftycdot|hatx|_infty+|b|_infty;.{displaymath}/;
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$key = q/{}$A_12${}/;
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$key = q/{}$Nleq128${}/;
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$key = q/{}$4.6cdot10^-7${}/;
$cached_env_img{$key} ='
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$key = q/{displaymath}X=Qleft(arrayccI;html_special_mark_amp;00;html_special_mark_amp;R^-1arrayright);;.{displaymath}/;
$cached_env_img{$key} ='
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$key = q/{}$AXpmXB=C${}/;
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$key = q/{}$s_i${}/;
$cached_env_img{$key} ='
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$key = q/{}$1(|hatR^-1|_infty|hatR|_infty)${}/;
$cached_env_img{$key} ='
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$key = q/{}$BA-lambdaI${}/;
$cached_env_img{$key} ='
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$key = q/{}$n-m${}/;
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$key = q/{}$mu${}/;
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$key = q/{}$ttANORM=120231${}/;
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$key = q/{}$vhat_i${}/;
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$key = q/{}$|B-B'|=10^-16${}/;
$cached_env_img{$key} ='
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$key = q/{displaymath}$H_1,H_2,ldots,H_b{displaymath}/;
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$key = q/{}$hatsigma_1geqcdotsgeqhatsigma_r${}/;
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$key = q/{}$T_1=Q_1Lambda_1Q_1^T${}/;
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$key = q/{}$hatSigma${}/;
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$key = q/{}$A=USigmaV^T${}/;
$cached_env_img{$key} ='
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$cached_env_img{$key} ='
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$key = q/{}$X^TA^TAX${}/;
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$key = q/{}$|deltainfnorm${}/;
$cached_env_img{$key} ='
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$key = q/{}$p(n)=10n${}/;
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$key = q/{}$n2${}/;
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$key = q/{displaymath}hatx=left(arrayc1.19911arrayright)cdot(1.1^2+99^2+11^2)^-12;rmso;|hatx|_2=1;;rmand;;x=left(arrayc11009arrayright){displaymath}/;
$cached_env_img{$key} ='
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$key = q/{}$d=Ax+By${}/;
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$key = q/{displaymath}A=U^TU;;rmor;;A=LL^Tmbox(inthesymmetriccase)<<1126>{displaymath}/;
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$key = q/{}$B=LL^T${}/;
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$key = q/{}$1:n-1${}/;
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$key = q/{}$C=L^-1AL^-T${}/;
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$key = q/{}$hatcalS${}/;
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$key = q/{}$c_1${}/;
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$key = q/{}$ttERRBD=1.5cdot10^-2${}/;
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$key = q/{}$T_21${}/;
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$key = q/{}$Lambda=mboxrmdiag(lambda_1,ldots,lambda_n)${}/;
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$key = q/{}$omegac${}/;
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$key = q/{}$calS_calI${}/;
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$key = q/{}$Sigma_1${}/;
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$key = q/{}$k+l${}/;
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$key = q/{}$C^2+S^2=I${}/;
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$key = q/{}$kd+1+i-j,j${}/;
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$key = q/{}$relgap_i=min_jneqi|lambda_i-lambda_j|(lambda_i+lambda_j)${}/;
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$key = q/{}$hatx${}/;
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$key = q/{displaymath}A=UDU^T;;rmor;;A=LDL^Tmbox(inthesymmetriccase)<<1145>{displaymath}/;
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$key = q/{}$a${}/;
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$key = q/{}$|tau-1|leq1${}/;
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$key = q/{displaymath}|hatlambda_i-lambda_i|leqttEERRBD(i);.{displaymath}/;
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$key = q/{}${sum_i=1^kbeta_ix_i${}/;
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$key = q/{}${hatx}${}/;
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$key = q/{}$|delta|${}/;
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$key = q/{}$-x${}/;
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$key = q/{}$kappa_infty${}/;
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$key = q/{displaymath}H^Hx=beta(1,0,ldots,0)^T{displaymath}/;
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$key = q/{displaymath}A=QSZ^H,quadB=QPZ^H{displaymath}/;
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$key = q/{}$hatX=[hatx_1,...,hatx_k]${}/;
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$key = q/{}$|E|_2${}/;
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$key = q/{}$j=1,ldots,n${}/;
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$key = q/{}$|x|_2=1${}/;
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$key = q/{}$sum_j=1^in_j${}/;
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$key = q/{displaymath}$Xhat{displaymath}/;
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$key = q/{}$|E|${}/;
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$key = q/{}$A_22^T${}/;
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$key = q/{}$i=1,ldots,l${}/;
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$key = q/{}$A=QHQ^T${}/;
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$key = q/{}$T=SLambdaS^T${}/;
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$key = q/{}$Sigma_2${}/;
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$key = q/{}$A${}/;
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$key = q/{}$r=b-Ahatx${}/;
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$key = q/{}$B^-1A${}/;
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$key = q/{}$|b-Ax|_2${}/;
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$key = q/{}$Z^HB^-1Z=I${}/;
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$key = q/{displaymath}kappa(D)=fracrule[-.25cm]0cm.5cmmax_ttILOleqileqttIHIttSCALE(i)min_ttILOleqileqttIHIttSCALE(i){displaymath}/;
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$key = q/{}$mu=1lambda${}/;
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$key = q/{}$|(A+E)hatx-(b+f)|_2${}/;
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$key = q/{displaymath}min_x|B^-1(d-Ax)|_2{displaymath}/;
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$key = q/{}$hatlambda_calI${}/;
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$key = q/{}$O(epsilon)${}/;
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$key = q/{displaymath}muAy=By.{displaymath}/;
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$key = q/{}$L_22${}/;
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$key = q/{displaymath}|r|_2=|b-Ax|_2=|c_2|_2.{displaymath}/;
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$key = q/{}$Q_1${}/;
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$key = q/{}$t${}/;
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$key = q/{}$|A^-1|${}/;
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$key = q/{displaymath}gap_calI=min_iincalIatopjnotincalI|lambda_i-lambda_j|{displaymath}/;
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$key = q/{}$X^HX=I${}/;
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$key = q/{}$1${}/;
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$key = q/{}$Ahatx${}/;
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$key = q/{displaymath}left(arrayccR_11;html_special_mark_amp;R_12arrayright)Z=left(arrayccT_11;html_special_mark_amp;0arrayright).{displaymath}/;
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$key = q/{}$ttANORM=3.300cdot10^4${}/;
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$key = q/{}$U=U_1U_2${}/;
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$key = q/{}$|f|_infty|binfnorm${}/;
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$key = q/{}$Sigma=mboxrmdiag(sigma_1,ldots,sigma_r)${}/;
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$key = q/{}$2cdotomega_infty${}/;
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$key = q/{}$Lambda${}/;
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$key = q/{}$|A|_infty=max_1leqileqmsum_j=1^n|a_ij|${}/;
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$key = q/{}$ILO=1${}/;
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$key = q/{}$d${}/;
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$key = q/{}$A=U^TU${}/;
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$key = q/{displaymath}A=Qleft(arraycR0arrayright)P^T,quadmgen,{displaymath}/;
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$key = q/{}$A^T${}/;
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$key = q/{}$epsiloncdotttABNRM${}/;
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$key = q/{}$fl(aoplusb)${}/;
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$key = q/{}$hatlambda_1leqcdotsleqhatlambda_n${}/;
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$key = q/{}$hatx_i${}/;
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$key = q/{}$AX+XB=C${}/;
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$key = q/{}$epsilon=${}/;
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$key = q/{}$s_calI${}/;
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$key = q/{}$y=f(z)${}/;
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$key = q/{}$A_23${}/;
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$key = q/{}$omega_inftyleqp(n)cdotepsilon${}/;
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$key = q/{}$|hatx|_2=1${}/;
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$key = q/{}$r${}/;
$cached_env_img{$key} ='
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$key = q/{}$Q^T${}/;
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$key = q/{}$mlln${}/;
$cached_env_img{$key} ='
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$key = q/{}$U_11${}/;
$cached_env_img{$key} ='
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$key = q/{displaymath}A=left(arrayccL;html_special_mark_amp;0arrayright)QquadLongleftrightarrowquadA^T=Q^Tleft(arraycL^T0arrayright).{displaymath}/;
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$key = q/{}$|x|_i=|x_i|${}/;
$cached_env_img{$key} ='
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$key = q/{}$b${}/;
$cached_env_img{$key} ='
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$key = q/{}$|T|_1${}/;
$cached_env_img{$key} ='
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$key = q/{}$|hatA-A|_p${}/;
$cached_env_img{$key} ='
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$key = q/{}$|hatx-x|_2${}/;
$cached_env_img{$key} ='
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$key = q/{}$epsilon_rmdoubleepsilon_rmsingle${}/;
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$key = q/{}$hatcalSI${}/;
$cached_env_img{$key} ='
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$key = q/{}$U_1${}/;
$cached_env_img{$key} ='
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$key = q/{}$A=USigmaV^H${}/;
$cached_env_img{$key} ='
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$key = q/{}$f_pq(m,n)${}/;
$cached_env_img{$key} ='
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$key = q/{}$y^HA=lambday^HB${}/;
$cached_env_img{$key} ='
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$key = q/{}$ttBNORM=120${}/;
$cached_env_img{$key} ='
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$key = q/{}$R${}/;
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$key = q/{displaymath}$T{displaymath}/;
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$key = q/{}$ttRNORM=8.843${}/;
$cached_env_img{$key} ='
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$key = q/{}$ttRCONDB=.8326${}/;
$cached_env_img{$key} ='
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$key = q/{}$beta_i${}/;
$cached_env_img{$key} ='
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$key = q/{displaymath}|hatlambda_i-lambda_i|leqttEERRBD;;.{displaymath}/;
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$key = q/{displaymath}|sigmahat_i-sigma_i|leqp(m,n)cdotepsiloncdotsigma_1=ttSERRBD;,{displaymath}/;
$cached_env_img{$key} ='
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$key = q/{}$C=L^-1AL^-H${}/;
$cached_env_img{$key} ='
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$key = q/{}$M;html_special_mark_gt;;html_special_mark_gt;N${}/;
$cached_env_img{$key} ='
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$key = q/{displaymath}A=RQquadmboxandquadB=ZTQ{displaymath}/;
$cached_env_img{$key} ='
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$key = q/{displaymath}T=bordermatrix;html_special_mark_amp;p-n;html_special_mark_amp;ncrn;html_special_mark_amp;0;html_special_mark_amp;T_12,quadmboxifquadnleqp{displaymath}/;
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$key = q/{}$sigma_1${}/;
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$key = q/{}$kappa_infty(A)equiv|A|_inftycdot|A^-1infnorm${}/;
$cached_env_img{$key} ='
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$key = q/{}$hatSigma_1^ThatSigma_1${}/;
$cached_env_img{$key} ='
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$key = q/{}${2x}${}/;
$cached_env_img{$key} ='
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$key = q/{}$V_2${}/;
$cached_env_img{$key} ='
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$key = q/{displaymath}x=R^-1_11(d_1-T_12y_2)quadmboxandquady=Z^Tleft(arrayc0y_2arrayright),{displaymath}/;
$cached_env_img{$key} ='
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$key = q/{}$f_k${}/;
$cached_env_img{$key} ='
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$key = q/{}$T=QPZ^T${}/;
$cached_env_img{$key} ='
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$key = q/{}$ttSLAMCH('E')=2^-24=5.961cdot10^-8${}/;
$cached_env_img{$key} ='
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$key = q/{}$kl${}/;
$cached_env_img{$key} ='
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$key = q/{}$A=U^T_AU_A${}/;
$cached_env_img{$key} ='
';
$key = q/{}$betax${}/;
$cached_env_img{$key} ='
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$key = q/{table}[b]labelclockspeedcentertabular|l||r|r|hline;html_special_mark_amp;multicolumn2c|ClockSpeedhlineCONVEXC-4640;html_special_mark_amp;135MHz;html_special_mark_amp;7.41nsCRAYC90;html_special_mark_amp;240MHz;html_special_mark_amp;4.167nsDEC3000-500XAlpha;html_special_mark_amp;200MHz;html_special_mark_amp;5.0nsIBMPOWER2model590;html_special_mark_amp;66MHz;html_special_mark_amp;15.15nsIBMRISCSys6000-550;html_special_mark_amp;42MHz;html_special_mark_amp;23.81nsSGIPOWERCHALLENGE;html_special_mark_amp;75MHz;html_special_mark_amp;13.33nshlinetabularcenter{table}/;
$cached_env_img{$key} ='
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$key = q/{}$beta_1=cdots=beta_k=0${}/;
$cached_env_img{$key} ='
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$key = q/{}$kl+ku${}/;
$cached_env_img{$key} ='
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$key = q/{}${hatu_i,,,iincalI}${}/;
$cached_env_img{$key} ='
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$key = q/{}$A^TX=B${}/;
$cached_env_img{$key} ='
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$key = q/{}$ku=1${}/;
$cached_env_img{$key} ='
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$key = q/{}$T_2=Q_2Lambda_2Q_2^T${}/;
$cached_env_img{$key} ='
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$key = q/{}$=1.5cdot10^-3${}/;
$cached_env_img{$key} ='
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$key = q/{}$kappa_2(B)${}/;
$cached_env_img{$key} ='
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$key = q/{figure}centerlinepsfigfigure=qrcray.eps,height=3.0in,width=4.0inlabelqrfx.fig{figure}/;
$cached_env_img{$key} ='
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$key = q/{}$1sqrt(x_i^HAx_i)^2+(x_i^HBx_i)^2${}/;
$cached_env_img{$key} ='
';
$key = q/{}$xne0${}/;
$cached_env_img{$key} ='
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$key = q/{}$fracrmrun-time(LAPACK~Driver~on~an~itn-by-itn~matrix)rmrun-time(DGEMM~used~to~multiply~two~itn-by-itn~matrices)${}/;
$cached_env_img{$key} ='
';
$key = q/{}$hatSigma_2^ThatSigma_2${}/;
$cached_env_img{$key} ='
';
$key = q/{}$alg${}/;
$cached_env_img{$key} ='
';
$key = q/{}$c=U^Tb=U_2^TU_1^Tb${}/;
$cached_env_img{$key} ='
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$key = q/{}$sigma_1geqcdotsgeqsigma_rgeq0${}/;
$cached_env_img{$key} ='
';
$key = q/{}$p+mgeqn;html_special_mark_gt;m${}/;
$cached_env_img{$key} ='
';
$key = q/{}$D^-1AD^-1${}/;
$cached_env_img{$key} ='
';
$key = q/{}${v_i,,,iincalI}${}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}|lambdahat_i-lambda_i|leqp(n)cdotepsiloncdotkappa_2(H)cdotlambda_i{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}x=hatx=left(arrayc38.4921.59-23.88arrayright);;,{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}$u_jj{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{}$dag${}/;
$cached_env_img{$key} ='
';
$key = q/{}$[0,R]${}/;
$cached_env_img{$key} ='
';
$key = q/{}$H=QSZ^H${}/;
$cached_env_img{$key} ='
';
$key = q/{}$epsilon|hatR|_infty${}/;
$cached_env_img{$key} ='
';
$key = q/{}$1+sum_j=1^i-1n_j${}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}$B{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}A+E=(hatU+deltahatU)hatSigma_1[0,hatR](hatQ+deltahatQ)^T;;rmand;;B+F=(hatV+deltahatV)hatSigma_2[0,hatR](hatQ+deltahatQ)^T{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{}$m-r;html_special_mark_lt;0${}/;
$cached_env_img{$key} ='
';
$key = q/{}$j^th${}/;
$cached_env_img{$key} ='
';
$key = q/{}$s=1${}/;
$cached_env_img{$key} ='
';
$key = q/{}$r=min(m,n)${}/;
$cached_env_img{$key} ='
';
$key = q/{}$4.504cdot10^-8${}/;
$cached_env_img{$key} ='
';
$key = q/{}$n|E|_2s_i${}/;
$cached_env_img{$key} ='
';
$key = q/{}$H,T${}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}A=left(arrayccQ_1;html_special_mark_amp;Q_2arrayright)left(arraycR0arrayright){displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{}$n${}/;
$cached_env_img{$key} ='
';
$key = q/{}$kd${}/;
$cached_env_img{$key} ='
';
$key = q/{}$left(arraycd_1d_2emat${}/;
$cached_env_img{$key} ='
';
$key = q/{}$(A+E)hatx=b+f${}/;
$cached_env_img{$key} ='
';
$key = q/{}$hatUhatSigma_1[0,hatR]hatQ^T${}/;
$cached_env_img{$key} ='
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$key = q/{displaymath}A^-1approxleft(arrayccc-.667;html_special_mark_amp;-1.333;html_special_mark_amp;1-.667;html_special_mark_amp;3.667;html_special_mark_amp;-21;html_special_mark_amp;-2;html_special_mark_amp;1arrayright);;rmand;;kappa_infty(A)=158.33;;.{displaymath}/;
$cached_env_img{$key} ='
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$key = q/{}$ABz=lambdaz${}/;
$cached_env_img{$key} ='
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$key = q/{tabular}|c|c|hlineBandmatrix$A$;html_special_mark_amp;BandstorageinarrayABhline$left(arrayccccca_11;html_special_mark_amp;a_12;html_special_mark_amp;;html_special_mark_amp;;html_special_mark_amp;a_21;html_special_mark_amp;a_22;html_special_mark_amp;a_23;html_special_mark_amp;;html_special_mark_amp;a_31;html_special_mark_amp;a_32;html_special_mark_amp;a_33;html_special_mark_amp;a_34;html_special_mark_amp;;html_special_mark_amp;a_42;html_special_mark_amp;a_43;html_special_mark_amp;a_44;html_special_mark_amp;a_45;html_special_mark_amp;;html_special_mark_amp;a_53;html_special_mark_amp;a_54;html_special_mark_amp;a_55arrayright)$;html_special_mark_amp;$arraycccccast;html_special_mark_amp;a_12;html_special_mark_amp;a_23;html_special_mark_amp;a_34;html_special_mark_amp;a_45a_11;html_special_mark_amp;a_22;html_special_mark_amp;a_33;html_special_mark_amp;a_44;html_special_mark_amp;a_55a_21;html_special_mark_amp;a_32;html_special_mark_amp;a_43;html_special_mark_amp;a_54;html_special_mark_amp;asta_31;html_special_mark_amp;a_42;html_special_mark_amp;a_53;html_special_mark_amp;ast;html_special_mark_amp;astarray$hline{tabular}/;
$cached_env_img{$key} ='
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$key = q/{table}[ht]labeltabdriveseigcentertabular||c|l||l|l||l|l||hlineTypeof;html_special_mark_amp;Functionandstoragescheme;html_special_mark_amp;multicolumn2c||Singleprecision;html_special_mark_amp;multicolumn2c||Doubleprecisioncline3-6problem;html_special_mark_amp;;html_special_mark_amp;real;html_special_mark_amp;complex;html_special_mark_amp;real;html_special_mark_amp;complexhlinehlineSEP;html_special_mark_amp;simpledriver;html_special_mark_amp;SSYEVindexSSYEV;html_special_mark_amp;CHEEVindexCHEEV;html_special_mark_amp;DSYEVindexDSYEV;html_special_mark_amp;ZHEEVindexZHEEV;html_special_mark_amp;divideandconquerdriver;html_special_mark_amp;SSYEVDindexSSYEVD;html_special_mark_amp;CHEEVDindexCHEEVD;html_special_mark_amp;DSYEVDindexDSYEVD;html_special_mark_amp;ZHEEVDindexZHEEVD;html_special_mark_amp;expertdriver;html_special_mark_amp;SSYEVXindexSSYEVX;html_special_mark_amp;CHEEVXindexCHEEVX;html_special_mark_amp;DSYEVXindexDSYEVX;html_special_mark_amp;ZHEEVXindexZHEEVXhline;html_special_mark_amp;simpledriver(packedstorage);html_special_mark_amp;SSPEVindexSSPEV;html_special_mark_amp;CHPEVindexCHPEV;html_special_mark_amp;DSPEVindexDSPEV;html_special_mark_amp;ZHPEVindexZHPEV;html_special_mark_amp;divideandconquerdriver;html_special_mark_amp;SSPEVDindexSSPEVD;html_special_mark_amp;CHPEVDindexCHPEVD;html_special_mark_amp;DSPEVDindexDSPEVD;html_special_mark_amp;ZHPEVDindexZHPEVD;html_special_mark_amp;hspace*.2in(packedstorage);html_special_mark_amp;;html_special_mark_amp;;html_special_mark_amp;;html_special_mark_amp;;html_special_mark_amp;expertdriver(packedstorage);html_special_mark_amp;SSPEVXindexSSPEVX;html_special_mark_amp;CHPEVXindexCHPEVX;html_special_mark_amp;DSPEVXindexDSPEVX;html_special_mark_amp;ZHPEVXindexZHPEVXhline;html_special_mark_amp;simpledriver(bandmatrix);html_special_mark_amp;SSBEVindexSSBEV;html_special_mark_amp;CHBEVindexCHBEV;html_special_mark_amp;DSBEVindexDSBEV;html_special_mark_amp;ZHBEVindexZHBEV;html_special_mark_amp;divideandconquerdriver;html_special_mark_amp;SSBEVDindexSSBEVD;html_special_mark_amp;CHBEVDindexCHBEVD;html_special_mark_amp;DSBEVDindexDSBEVD;html_special_mark_amp;ZHBEVDindexZHBEVD;html_special_mark_amp;hspace*.2in(bandmatrix);html_special_mark_amp;;html_special_mark_amp;;html_special_mark_amp;;html_special_mark_amp;;html_special_mark_amp;expertdriver(bandmatrix);html_special_mark_amp;SSBEVXindexSSBEVX;html_special_mark_amp;CHBEVXindexCHBEVX;html_special_mark_amp;DSBEVXindexDSBEVX;html_special_mark_amp;ZHBEVXindexZHBEVXhline;html_special_mark_amp;simpledriver(tridiagonalmatrix);html_special_mark_amp;SSTEVindexSSTEV;html_special_mark_amp;;html_special_mark_amp;DSTEVindexDSTEV;html_special_mark_amp;;html_special_mark_amp;divideandconquerdriver;html_special_mark_amp;SSTEVDindexSSTEVD;html_special_mark_amp;;html_special_mark_amp;DSTEVDindexDSTEVD;html_special_mark_amp;;html_special_mark_amp;hspace*.2in(tridiagonalmatrix);html_special_mark_amp;;html_special_mark_amp;;html_special_mark_amp;;html_special_mark_amp;;html_special_mark_amp;expertdriver(tridiagonalmatrix);html_special_mark_amp;SSTEVXindexSSTEVX;html_special_mark_amp;;html_special_mark_amp;DSTEVXindexDSTEVX;html_special_mark_amp;hlinehlineNEP;html_special_mark_amp;simpledriverforSchurfactorization;html_special_mark_amp;SGEESindexSGEES;html_special_mark_amp;CGEESindexCGEES;html_special_mark_amp;DGEESindexDGEES;html_special_mark_amp;ZGEESindexZGEES;html_special_mark_amp;expertdriverforSchurfactorization;html_special_mark_amp;SGEESXindexSGEESX;html_special_mark_amp;CGEESXindexCGEESX;html_special_mark_amp;DGEESXindexDGEESX;html_special_mark_amp;ZGEESXindexZGEESX;html_special_mark_amp;simpledriverforeigenvaluesvectors;html_special_mark_amp;SGEEVindexSGEEV;html_special_mark_amp;CGEEVindexCGEEV;html_special_mark_amp;DGEEVindexDGEEV;html_special_mark_amp;ZGEEVindexZGEEV;html_special_mark_amp;expertdriverforeigenvaluesvectors;html_special_mark_amp;SGEEVXindexSGEEVX;html_special_mark_amp;CGEEVXindexCGEEVX;html_special_mark_amp;DGEEVXindexDGEEVX;html_special_mark_amp;ZGEEVXindexZGEEVXhlinehlineSVD;html_special_mark_amp;singularvaluesvectors;html_special_mark_amp;SGESVDindexSGESVD;html_special_mark_amp;CGESVDindexCGESVD;html_special_mark_amp;DGESVDindexDGESVD;html_special_mark_amp;ZGESVDindexZGESVDhlinetabularcenter{table}/;
$cached_env_img{$key} ='
';
$key = q/{}$lambda_i${}/;
$cached_env_img{$key} ='
';
$key = q/{}$hatA${}/;
$cached_env_img{$key} ='
';
$key = q/{}$relgap_i=min_jneqi|sigma_i-sigma_j|(sigma_i+sigma_j)${}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}A=Qleft(arrayc0Larrayright),quadmboxif$mgeqn$,{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{}$R_22${}/;
$cached_env_img{$key} ='
';
$key = q/{}$kappa_2(H)${}/;
$cached_env_img{$key} ='
';
$key = q/{}$Q^TQ=I${}/;
$cached_env_img{$key} ='
';
$key = q/{}$kl,kullmin(m,n)${}/;
$cached_env_img{$key} ='
';
$key = q/{}$H_i${}/;
$cached_env_img{$key} ='
';
$key = q/{}$mu=0${}/;
$cached_env_img{$key} ='
';
$key = q/{}$B=S^TS${}/;
$cached_env_img{$key} ='
';
1;
.