# LaTeX2HTML 95 (Thu Jan 19 1995)
# Associate image original text (scrambled) with physical files.

$key = q/{_inline}$tildeN_jac${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img101.gif">'; 
$key = q/{_inline}$(N-A)u^m${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img94.gif">'; 
$key = q/{_inline}$1.0${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img262.gif">'; 
$key = q/{_inline}$A_22x_2=ldots${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img46.gif">'; 
$key = q/{_inline}$(A+tildeN-N)u=f${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img96.gif">'; 
$key = q/{_inline}$|NtildeN^-1|=|NtildeN^-1-I+I|leq1+Ceps${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img150.gif">'; 
$key = q/{_inline}$|x_2|leq1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img138.gif">'; 
$key = q/{_inline}$p_i0=0${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img112.gif">'; 
$key = q/{_inline}$V_k=;SPM_lt;v_1,v_2,ldots,v_k;SPM_gt;${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img161.gif">'; 
$key = q/{_inline}$III_nr${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img53.gif">'; 
$key = q/{_inline}$N_jac${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img79.gif">'; 
$key = q/{_inline}$A_11^-1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img43.gif">'; 
$key = q/{_inline}$tildeA_iitildeu_i=g_i${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img127.gif">'; 
$key = q/{_inline}$A_21${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img39.gif">'; 
$key = q/{_inline}$N_gs${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img78.gif">'; 
$key = q/{_inline}$v_r${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img74.gif">'; 
$key = q/{_inline}$x=left[arraycx_1x_2arrayright]${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img133.gif">'; 
$key = q/{_inline}$AN^-1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img147.gif">'; 
$key = q/{_inline}$|B|=sqrtrho(B^TB)=sqrtrho(mboxdiag(D_1^TD_1,ldots,D_n^TD_n))=max{sqrtrho(D_1^TD_1),ldots,sqrtrho(D_n^TD_n)}=max{|D_1|,ldots|D_n|}${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img141.gif">'; 
$key = q/{_inline}$A_11x_1=ldots${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img45.gif">'; 
$key = q/{_inline}$v_2^m+1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img69.gif">'; 
$key = q/{_inline}$S(V^n,P^n)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img56.gif">'; 
$key = q/{_inline}$A_ii${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img200.gif">'; 
$key = q/{_inline}$p(A_ii)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img115.gif">'; 
$key = q/{_inline}$|x_1|leq1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img137.gif">'; 
$key = q/{_inline}$tildeA_11^-1t_1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img106.gif">'; 
$key = q/{_inline}${v_i}_i=1,ldots,k${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img167.gif">'; 
$key = q/{_inline}$x_kinS_k${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img169.gif">'; 
$key = q/{_inline}$P^n+1=P^n+DeltaP${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img27.gif">'; 
$key = q/{_inline}$tildeNu^m+1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img95.gif">'; 
$key = q/{_inline}$mboxRe=1-5${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img213.gif">'; 
$key = q/{_inline}$10^-1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img242.gif">'; 
$key = q/{_inline}$B=mboxdiag(D_1,D_2,ldots,D_n)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img140.gif">'; 
$key = q/{_inline}$V_k${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img168.gif">'; 
$key = q/{_inline}$0.02${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img219.gif">'; 
$key = q/{_inline}$|x|leq1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img136.gif">'; 
$key = q/{_inline}$fracsqrtkappa-1sqrtkappa+1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img120.gif">'; 
$key = q/{_inline}$eps${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img156.gif">'; 
$key = q/{_inline}$kappa(AtildeN^-1)=kappa(AN^-1NtildeN^-1)leqkappa(AN^-1)cdotkappa(NtildeN^-1)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img154.gif">'; 
$key = q/{_inline}$1leqileqk${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img189.gif">'; 
$key = q/{_inline}$f-Ax_kperpv_i${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img170.gif">'; 
$key = q/{_inline}$barV^star_2=barV'^star_2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img60.gif">'; 
$key = q/{_inline}$S_k=;SPM_lt;s_1,s_2,ldots,s_k;SPM_gt;${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img159.gif">'; 
$key = q/{_inline}$g_i${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img129.gif">'; 
$key = q/{table}[htb]centertabular||c|c|c|c||hlinemulticolumn4||c||emPoisseuilleflowhlineemTotal;SPM_amp;emMomentum;SPM_amp;emPressure;SPM_amp;emOtherhline_inline$94.0$_inline;SPM_amp;_inline$46.5(407)$_inline;SPM_amp;_inline$21.0(395)$_inline;SPM_amp;_inline$24.4$_inlinehlinehlinemulticolumn4||c||emCylinderproblemhlineemTotal;SPM_amp;emMomentum;SPM_amp;emPressure;SPM_amp;emOtherhline_inline$128.0$_inline;SPM_amp;_inline$31.6(140)$_inline;SPM_amp;_inline$48.9(497)$_inline;SPM_amp;_inline$44.0$_inlinehlinetabularcenterlabeltab-single{table}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img254.gif">'; 
$key = q/{_inline}$tildeA_ii^-1=p(A_ii)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img116.gif">'; 
$key = q/{_inline}$tildeA_ii=L_iU_i${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img199.gif">'; 
$key = q/{_inline}$v_k+1=As_k+1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img186.gif">'; 
$key = q/{_inline}$epsilon=10^-1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img284.gif">'; 
$key = q/{_inline}$A_12v_2^m${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img65.gif">'; 
$key = q/{_inline}$s_k+1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img198.gif">'; 
$key = q/{_inline}$s_i${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img160.gif">'; 
$key = q/{_inline}$r_k${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img185.gif">'; 
$key = q/{_inline}$V^n+1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img28.gif">'; 
$key = q/{figure}[htb]centerlinepsfigfile=staggered.eps,width=13.0cm,height=3.7cmlabelfig-staggered{figure}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img11.gif">'; 
$key = q/{figure}[htb]centerlinetabularccpsfigfile=momalpha.eps,width=6.0cm,height=4.9cm;SPM_amp;psfigfile=palpha.eps,width=6.0cm,height=4.9cm(a);SPM_amp;(b)tabularlabelfig-alpha{figure}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img277.gif">'; 
$key = q/{_inline}$0.975${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img230.gif">'; 
$key = q/{_inline}$A_22${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img37.gif">'; 
$key = q/{_inline}$I_nr${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img51.gif">'; 
$key = q/{_inline}$0.95${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img233.gif">'; 
$key = q/{_inline}$[0,1]times[0,1]${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img221.gif">'; 
$key = q/{_inline}$v_1^m+1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img68.gif">'; 
$key = q/{_inline}$V^star${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img32.gif">'; 
$key = q/{_inline}$v_2^m${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img44.gif">'; 
$key = q/{_inline}$80times80${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img222.gif">'; 
$key = q/{_inline}$sigma_xy=tau_0${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img217.gif">'; 
$key = q/{_inline}$Ax_kinV_k${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img173.gif">'; 
$key = q/{_inline}$I_r${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img52.gif">'; 
$key = q/{_inline}$AtildeN^-1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img119.gif">'; 
$key = q/{_inline}$10^-2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img265.gif">'; 
$key = q/{_inline}$I-NtildeN^-1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img142.gif">'; 
$key = q/{_inline}$varepsilon${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img292.gif">'; 
$key = q/{_inline}$Q^T${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img89.gif">'; 
$key = q/{_inline}$|I-NtildeN^-1|=sup_|x|leq1|(I-NtildeN^-1)x|leqsup_|x|leq1left(|(I-A_11tildeA_11^-1)x_1|+|(I-A_22tildeA_22^-1)A_21tildeA_11^-1x_1|+|(I-A_22tildeA_22^-1)x_2|right)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img135.gif">'; 
$key = q/{_inline}$r=Q^TN^-1f-Q^TN^-1AQv${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img208.gif">'; 
$key = q/{_inline}$32${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img195.gif">'; 
$key = q/{_inline}$lambda_i=(f,v_i)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img175.gif">'; 
$key = q/{_inline}$C=2+|A_21tildeA_11^-1|${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img139.gif">'; 
$key = q/{_inline}$Q=left[arrayc0Iarrayright]${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img87.gif">'; 
$key = q/{_inline}$Box${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img155.gif">'; 
$key = q/{_inline}$|I-NtildeN^-1|=max_i|I-A_iitildeA_ii^-1|leqeps${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img144.gif">'; 
$key = q/{_inline}$sigma_xx=0${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img216.gif">'; 
$key = q/{_inline}$0.0${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img278.gif">'; 
$key = q/{_inline}$1.5-2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img282.gif">'; 
$key = q/{_inline}$i=1,ldotsk${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img171.gif">'; 
$key = q/{_inline}$0.95)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img229.gif">'; 
$key = q/{_inline}$epsilon=10^-2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img267.gif">'; 
$key = q/{_inline}$P^n${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img13.gif">'; 
$key = q/{_inline}$v_k+1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img187.gif">'; 
$key = q/{figure}[htb]centerlinepsfigfile=molecule.eps,width=10.0cm,height=5.7cmlabelfig-molecule{figure}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img21.gif">'; 
$key = q/{_inline}$S(V^n,P^n)V^star=f${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img62.gif">'; 
$key = q/{_inline}$x_k+1=x_k+(f,v_k+1)s_k+1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img180.gif">'; 
$key = q/{_inline}$V^n${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img12.gif">'; 
$key = q/{_inline}$u=fractau_0mucdoty${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img215.gif">'; 
$key = q/{_inline}$s_k+1=tildeN^-1r_k${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img196.gif">'; 
$key = q/{_inline}$|star|${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img149.gif">'; 
$key = q/{_inline}$kappa(NtildeN^-1)=|NtildeN^-1|cdot|(NtildeN^-1)^-1|leqfrac1+Cepsilon1-Cepsilon${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img153.gif">'; 
$key = q/{_inline}$p(A_ii)r_0${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img111.gif">'; 
$key = q/{_inline}$v_nr${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img75.gif">'; 
$key = q/{_inline}$S_22${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img61.gif">'; 
$key = q/{_inline}$p=tildeN_gs^-1t${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img104.gif">'; 
$key = q/{_inline}$x_k=sum_i=1ldotsk(f,v_i)s_i${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img179.gif">'; 
$key = q/{_inline}$As_k+1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img184.gif">'; 
$key = q/{_inline}$mboxRe=2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img214.gif">'; 
$key = q/{_inline}$|x|leqleft|left[arraycx_10arrayright]right|+left|left[arrayc0x_2arrayright]right|=|x_1|+|x_2|${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img134.gif">'; 
$key = q/{_inline}$S_k${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img194.gif">'; 
$key = q/{_inline}$t^n${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img14.gif">'; 
$key = q/{_inline}$tau_0=mupartialupartialy${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img212.gif">'; 
$key = q/{_inline}$A_11${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img36.gif">'; 
$key = q/{figure}[htb]centerlinepsfigfile=smulti.eps,width=12.0cm,height=6.0cm,angle=-90labelfig-s{figure}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img220.gif">'; 
$key = q/{table}[htb]centertabular||c|c|c|c|c||hlinemulticolumn5||c||Poisseuilleflowhline;SPM_amp;;SPM_amp;multicolumn3|c||decompositioncline3-5;SPM_amp;_inline$epsilon$_inline;SPM_amp;_inline$2times2$_inline;SPM_amp;_inline$4times4$_inline;SPM_amp;_inline$5times5$_inlinehlineI;SPM_amp;_inline$10^-8$_inline;SPM_amp;_inline$333.6(101)$_inline;SPM_amp;_inline$190.8(120)$_inline;SPM_amp;_inline$171.3(129)$_inline;SPM_amp;_inline$10^-4$_inline;SPM_amp;_inline$147.3(102)$_inline;SPM_amp;_inline$90.5(121)$_inline;SPM_amp;_inline$87.5(129)$_inlinehlineII;SPM_amp;_inline$10^-4$_inline;SPM_amp;_inline$120.1(89)$_inline;SPM_amp;_inline$81.0(106)$_inline;SPM_amp;_inline$82.8(116)$_inline;SPM_amp;_inline$10^-2$_inline;SPM_amp;_inline$55.6(89)$_inline;SPM_amp;_inline$50.6(108)$_inline;SPM_amp;_inline$56.6(117)$_inline;SPM_amp;_inline$10^-1$_inline;SPM_amp;_inline$45.3(111)$_inline;SPM_amp;_inline$49.9(136)$_inline;SPM_amp;_inline$57.1(146)$_inlinehlineIII;SPM_amp;RIBLUD(_inline$0.95$_inline)post+GCR(trunc);SPM_amp;_inline$51.5(241)$_inline;SPM_amp;_inline$78.8(281)$_inline;SPM_amp;_inline$92.5(295)$_inline;SPM_amp;RIBLUD(_inline$0.95$_inline)post+GCR(restart);SPM_amp;_inline$42.8(241)$_inline;SPM_amp;_inline$65.8(281)$_inline;SPM_amp;_inline$86.4(295)$_inlinehlinehlinemulticolumn5||c||Cylinderproblemhline;SPM_amp;;SPM_amp;multicolumn3|c||no.ofblockscline3-5;SPM_amp;_inline$epsilon$_inline;SPM_amp;_inline$2$_inline;SPM_amp;_inline$4$_inline;SPM_amp;_inline$8$_inlinehlineI;SPM_amp;_inline$10^-8$_inline;SPM_amp;_inline$146.6(37)$_inline;SPM_amp;_inline$145.9(49)$_inline;SPM_amp;_inline$113.6(49)$_inline;SPM_amp;_inline$10^-4$_inline;SPM_amp;_inline$78.6(38)$_inline;SPM_amp;_inline$80.7(49)$_inline;SPM_amp;_inline$63.0(49)$_inlinehlineII;SPM_amp;_inline$10^-4$_inline;SPM_amp;_inline$58.4(37)$_inline;SPM_amp;_inline$65.7(47)$_inline;SPM_amp;_inline$53.0(47)$_inline;SPM_amp;_inline$10^-2$_inline;SPM_amp;_inline$43.5(38)$_inline;SPM_amp;_inline$49.3(47)$_inline;SPM_amp;_inline$42.4(47)$_inline;SPM_amp;_inline$10^-1$_inline;SPM_amp;_inline$47.5(48)$_inline;SPM_amp;_inline$52.5(56)$_inline;SPM_amp;_inline$59.8(56)$_inlinehlineIII;SPM_amp;RIBLUD(_inline$0.95$_inline)post+GCR(trunc);SPM_amp;_inline$28.4(85)$_inline;SPM_amp;_inline$30.8(86)$_inline;SPM_amp;_inline$30.8(86)$_inline;SPM_amp;RIBLUD(_inline$0.95$_inline)post+GCR(restart);SPM_amp;_inline$26.7(85)$_inline;SPM_amp;_inline$29.1(86)$_inline;SPM_amp;_inline$29.0(86)$_inlinehlinetabularcenterlabeltab-multi-mom{table}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img255.gif">'; 
$key = q/{_inline}$u^m=0${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img197.gif">'; 
$key = q/{_inline}$0.1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img259.gif">'; 
$key = q/{_inline}$s_k+1=r_k${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img193.gif">'; 
$key = q/{_inline}$|g_i-A_iitildeA_ii^-1g_i|=|(I-A_iitildeA_ii^-1)g_i|leqepsilon|g_i|${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img128.gif">'; 
$key = q/{_inline}$|(NtildeN^-1)^-1|=|(NtildeN^-1)^-1(I-NtildeN^-1)+I|leq1+|(NtildeN^-1)^-1|Ceps${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img151.gif">'; 
$key = q/{_inline}$r_k+1=r_k-(f,v_k+1)v_k+1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img182.gif">'; 
$key = q/{_inline}$tildeN_gs${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img100.gif">'; 
$key = q/{_inline}$DeltaP${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img25.gif">'; 
$key = q/{_inline}$v_i${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img188.gif">'; 
$key = q/{figure}[htb]centerlinetabularccpsfigfile=cyl.eps,width=6.0cm,height=3.0cm;SPM_amp;psfigfile=gridmulti.eps,width=6.0cm,height=3.0cm(a);SPM_amp;(b)psfigfile=gridsingle.eps,width=6.0cm,height=3.0cm;SPM_amp;(c);SPM_amp;tabularlabelfig-geom{figure}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img218.gif">'; 
$key = q/{_inline}$tildeA_ii${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img103.gif">'; 
$key = q/{figure}[htb]centerlinepsfigfile=twoblocks.eps,width=13.0cm,height=6.6cmlabelfig-twoblocks{figure}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img55.gif">'; 
$key = q/{_inline}$|r_k|leqepsilon|r_0|${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img209.gif">'; 
$key = q/{_inline}$N^-1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img41.gif">'; 
$key = q/{_inline}$|I-A_iitildeA_ii^-1|leqeps${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img130.gif">'; 
$key = q/{_inline}$III_r${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img54.gif">'; 
$key = q/{_inline}$Qv=left[arrayc0varrayright]${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img88.gif">'; 
$key = q/{_inline}$v=Deltap${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img34.gif">'; 
$key = q/{_inline}$r_k=f-Ax_k${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img181.gif">'; 
$key = q/{_inline}$D_i=I-A_iitildeA_ii^-1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img143.gif">'; 
$key = q/{_inline}$v_1^m${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img70.gif">'; 
$key = q/{_inline}$Cepsilon;SPM_lt;1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img152.gif">'; 
$key = q/{_inline}$x_0=0${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img164.gif">'; 
$key = q/{_inline}$G_1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img2.gif">'; 
$key = q/{_inline}$As_i=v_i${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img177.gif">'; 
$key = q/{_inline}$M_1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1.gif">'; 
$key = q/{_inline}$|f-Ax_k|_2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img165.gif">'; 
$key = q/{_inline}$10^-4${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img241.gif">'; 
$key = q/{_inline}$tildeN${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img131.gif">'; 
$key = q/{_inline}$u^m${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img80.gif">'; 
$key = q/{_inline}$u=left[arraycwvarrayright]${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img83.gif">'; 
$key = q/{_inline}$A_12${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img38.gif">'; 
$key = q/{_inline}$p_i=p(A_ii)v_i${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img114.gif">'; 
$key = q/{_inline}$mboxdiv,u=0${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img16.gif">'; 

1;

