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amg4psblas
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amg4psblas/docs/html/images.pl

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# LaTeX2HTML 2002-2-1 (1.71)
# Associate images original text with physical files.
$key = q/w=M^{-1}v;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="87" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img60.png"
ALT="$w=M^{-1}v$">|;
$key = q/w;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="17" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img87.png"
ALT="$w$">|;
$key = q/W_i^{delta};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="31" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img26.png"
ALT="$W_i^{\delta}$">|;
$key = q/{displaymath}M_{2LA}^{-1}=M_{C}^{-1}+M_{1L}^{-1}.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="165" HEIGHT="32" BORDER="0"
SRC="|."$dir".q|img52.png"
ALT="\begin{displaymath}
M_{2LA}^{-1} = M_{C}^{-1} + M_{1L}^{-1}.
\end{displaymath}">|;
$key = q/M_{1L}^{-1};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="42" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img54.png"
ALT="$M_{1L}^{-1}$">|;
$key = q/M_l;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="27" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img64.png"
ALT="$M_l$">|;
$key = q/W;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="24" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img10.png"
ALT="$W$">|;
$key = q/W_i^0subsetW;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="73" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img12.png"
ALT="$W_i^0 \subset W$">|;
$key = q/E={(i,j):a_{ij}neq0};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="162" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img6.png"
ALT="$E=\{(i,j) : a_{ij} \neq 0\}$">|;
$key = q/nlev;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="37" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img61.png"
ALT="$nlev$">|;
$key = q/A_i^deltaw_i=v_i;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="80" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img31.png"
ALT="$A_i^\delta w_i = v_i$">|;
$key = q/M_{1L};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="38" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img48.png"
ALT="$M_{1L}$">|;
$key = q/R_i^delta;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="25" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img38.png"
ALT="$R_i^\delta$">|;
$key = q/op(M^{-1})=M^{-T};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="135" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img98.png"
ALT="$op(M^{-1}) = M^{-T}$">|;
$key = q/W_i^{delta-1};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="48" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img15.png"
ALT="$W_i^{\delta-1}$">|;
$key = q/cup_{i=1}^mW_i^0=W;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="107" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img13.png"
ALT="$\cup_{i=1}^m W_i^0 = W$">|;
$key = q/delta=0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="45" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img42.png"
ALT="$\delta=0$">|;
$key = q/rinW;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="53" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img70.png"
ALT="$r \in W$">|;
$key = q/theta=0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="45" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img86.png"
ALT="$\theta = 0$">|;
$key = q/{displaymath}Ax=b,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="57" HEIGHT="30" BORDER="0"
SRC="|."$dir".q|img1.png"
ALT="\begin{displaymath}
Ax=b,
\end{displaymath}">|;
$key = q/Re^{n_i^delta};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="32" HEIGHT="24" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img23.png"
ALT="$\Re^{n_i^\delta}$">|;
$key = q/R_CinRe^{n_Ctimesn};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="101" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img46.png"
ALT="$R_C \in \Re^{n_C \times n}$">|;
$key = q/y;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="14" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img96.png"
ALT="$y$">|;
$key = q/{displaymath}A_C=R_CAR_C^T{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="109" HEIGHT="31" BORDER="0"
SRC="|."$dir".q|img47.png"
ALT="\begin{displaymath}
A_C=R_C A R_C^T
\end{displaymath}">|;
$key = q/l;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="10" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img62.png"
ALT="$l$">|;
$key = q/v_i=R_i^{delta}v;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="71" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img29.png"
ALT="$v_i = R_i^{\delta} v$">|;
$key = q/N_r;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="26" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img69.png"
ALT="$N_r$">|;
$key = q/P_C=R_C^T;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="75" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img75.png"
ALT="$P_C=R_C^T$">|;
$key = q/{displaymath}M_{2LH-PRE}^{-1}=M_{C}^{-1}+left(I-M_{C}^{-1}Aright)M_{1L}^{-1}.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="308" HEIGHT="33" BORDER="0"
SRC="|."$dir".q|img56.png"
ALT="\begin{displaymath}
M_{2LH-PRE}^{-1} = M_{C}^{-1} + \left( I - M_{C}^{-1}A \right) M_{1L}^{-1}.
\end{displaymath}">|;
$key = q/v_i^{delta}inRe^{n_i^delta};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="70" HEIGHT="43" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img20.png"
ALT="$v_i^{\delta} \in \Re^{n_i^\delta}$">|;
$key = q/{displaymath}M_{RAS}^{-1}=sum_{i=1}^m(tilde{R}_i^0)^T(A_i^delta)^{-1}R_i^{delta}.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="216" HEIGHT="58" BORDER="0"
SRC="|."$dir".q|img40.png"
ALT="\begin{displaymath}
M_{RAS}^{-1}= \sum_{i=1}^m (\tilde{R}_i^0)^T
(A_i^\delta)^{-1} R_i^{\delta}.
\end{displaymath}">|;
$key = q/A_l;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="22" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img63.png"
ALT="$A_l$">|;
$key = q/n_C;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="26" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img45.png"
ALT="$n_C$">|;
$key = q/W_i^delta;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="30" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img17.png"
ALT="$W_i^\delta$">|;
$key = q/A_i^delta;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="25" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img28.png"
ALT="$A_i^\delta$">|;
$key = q/{displaymath}M_{AS}^{-1}=sum_{i=1}^m(R_i^{delta})^T(A_i^delta)^{-1}R_i^{delta},{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="206" HEIGHT="58" BORDER="0"
SRC="|."$dir".q|img27.png"
ALT="\begin{displaymath}
M_{AS}^{-1}= \sum_{i=1}^m (R_i^{\delta})^T
(A_i^\delta)^{-1} R_i^{\delta},
\end{displaymath}">|;
$key = q/delta>0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="45" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img8.png"
ALT="$\delta &gt; 0$">|;
$key = q/w_i;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="23" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img32.png"
ALT="$w_i$">|;
$key = q/w=sum_{i=1}^m(R_i^{delta})^Tw_i;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="144" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img33.png"
ALT="$w = \sum_{i=1}^m (R_i^{\delta})^T w_i$">|;
$key = q/p;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img34.png"
ALT="$p$">|;
$key = q/A_i^delta=R_i^deltaA(R_i^delta)^TinRe^{n_i^deltatimesn_i^delta};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="201" HEIGHT="43" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img25.png"
ALT="$A_i^\delta=R_i^\delta A (R_i^\delta)^T \in
\Re^{n_i^\delta \times n_i^\delta}$">|;
$key = q/thetain[0,1];MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="69" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img72.png"
ALT="$\theta \in [0,1]$">|;
$key = q/A=(a_{ij})inRe^{ntimesn};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="137" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img3.png"
ALT="$A=(a_{ij}) \in \Re^{n \times n}$">|;
$key = q/tilde{R}_i^0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="25" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img37.png"
ALT="$\tilde{R}_i^0$">|;
$key = q/M_{2L-A}^{-1};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="59" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img53.png"
ALT="$M_{2L-A}^{-1}$">|;
$key = q/{displaymath}P_C=SP,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="73" HEIGHT="30" BORDER="0"
SRC="|."$dir".q|img81.png"
ALT="\begin{displaymath}
P_C = S P,
\end{displaymath}">|;
$key = q/M_{C};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="32" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img51.png"
ALT="$M_{C}$">|;
$key = q/{displaymath}N_r=left{sinW:|a_{rs}|>thetasqrt{|a_{rr}a_{ss}|}right}cupleft{rright},{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="319" HEIGHT="38" BORDER="0"
SRC="|."$dir".q|img71.png"
ALT="\begin{displaymath}N_r = \left\{s \in W: \vert a_{rs}\vert &gt; \theta \sqrt{\vert a_{rr}a_{ss}\vert} \right\}
\cup \left\{ r \right\} ,
\end{displaymath}">|;
$key = q/R_i^{delta};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="25" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img22.png"
ALT="$R_i^{\delta}$">|;
$key = q/R_C;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="29" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img67.png"
ALT="$R_C$">|;
$key = q/>0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img92.png"
ALT="$&gt;0$">|;
$key = q/(tilde{R}_i^0)^TinRe^{n_i^deltatimesn};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="118" HEIGHT="43" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img36.png"
ALT="$(\tilde{R}_i^0)^T \in \Re^{n_i^\delta \times n}$">|;
$key = q/A_1=A;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="61" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img65.png"
ALT="$A_1=A$">|;
$key = q/M;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="23" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img59.png"
ALT="$M$">|;
$key = q/x;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img95.png"
ALT="$x$">|;
$key = q/G=(W,E);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="93" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img4.png"
ALT="$G=(W,E)$">|;
$key = q/{displaymath}array{{l}w=M_{1L}^{-1}v,z=w+M_{C}^{-1}(v-Aw);array{{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="177" HEIGHT="51" BORDER="0"
SRC="|."$dir".q|img55.png"
ALT="\begin{displaymath}
\begin{array}{l}
w = M_{1L}^{-1} v, \\\\
z = w + M_{C}^{-1} (v-Aw);
\end{array}\end{displaymath}">|;
$key = q/P;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="18" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img79.png"
ALT="$P$">|;
$key = q/A_C;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="29" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img43.png"
ALT="$A_C$">|;
$key = q/n_i^delta;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="22" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img16.png"
ALT="$n_i^\delta$">|;
$key = q/M^{-1});MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="48" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img99.png"
ALT="$M^{-1})$">|;
$key = q/{displaymath}M_{C}^{-1}=R_C^TA_C^{-1}R_C,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="144" HEIGHT="32" BORDER="0"
SRC="|."$dir".q|img49.png"
ALT="\begin{displaymath}
M_{C}^{-1}= R_C^T A_C^{-1} R_C,
\end{displaymath}">|;
$key = q/i;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="10" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img73.png"
ALT="$i$">|;
$key = q/R_i^{delta}inRe^{n_i^deltatimesn};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="93" HEIGHT="43" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img18.png"
ALT="$R_i^{\delta} \in
\Re^{n_i^\delta \times n}$">|;
$key = q/in[0,1];MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="56" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img90.png"
ALT="$\in [0, 1]$">|;
$key = q/{displaymath}array{{l}w=M_{C}^{-1}v,z=w+M_{1L}^{-1}(v-Aw),array{{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="177" HEIGHT="51" BORDER="0"
SRC="|."$dir".q|img57.png"
ALT="\begin{displaymath}
\begin{array}{l}
w = M_{C}^{-1} v , \\\\
z = w + M_{1L}^{-1} (v-Aw) ,
\end{array}\end{displaymath}">|;
$key = q/p,t;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img35.png"
ALT="$p,t$">|;
$key = q/Re^n;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="26" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img24.png"
ALT="$\Re^n$">|;
$key = q/t;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="11" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img89.png"
ALT="$t$">|;
$key = q/PinRe^{ntimesn_C};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="90" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img76.png"
ALT="$P \in \Re^{n \times n_C}$">|;
$key = q/S;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="16" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img82.png"
ALT="$S$">|;
$key = q/D^{-1}A;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="50" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img85.png"
ALT="$D^{-1}A$">|;
$key = q/M_{C}^{-1};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="42" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img50.png"
ALT="$M_{C}^{-1}$">|;
$key = q/v;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img21.png"
ALT="$v$">|;
$key = q/R_C^T;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="29" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img68.png"
ALT="$R_C^T$">|;
$key = q/delta;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="13" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img9.png"
ALT="$\delta$">|;
$key = q/ge0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img88.png"
ALT="$\ge 0$">|;
$key = q/{displaymath}M_{2LH-POST}^{-1}=M_{1L}^{-1}+left(I-M_{1L}^{-1}Aright)M_{C}^{-1}.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="317" HEIGHT="33" BORDER="0"
SRC="|."$dir".q|img58.png"
ALT="\begin{displaymath}
M_{2LH-POST}^{-1} = M_{1L}^{-1} + \left( I - M_{1L}^{-1}A \right) M_{C}^{-1}.
\end{displaymath}">|;
$key = q/op;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="22" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img94.png"
ALT="$op$">|;
$key = q/G;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="18" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img7.png"
ALT="$G$">|;
$key = q/omega;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img84.png"
ALT="$\omega$">|;
$key = q/P_C;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="27" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img78.png"
ALT="$P_C$">|;
$key = q/W_C;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="32" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img44.png"
ALT="$W_C$">|;
$key = q/W_i^0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="31" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img74.png"
ALT="$W_i^0$">|;
$key = q/op(M^{-1})=M^{-1};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="132" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img97.png"
ALT="$op(M^{-1}) = M^{-1}$">|;
$key = q/W={1,2,ldots,n};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="138" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img5.png"
ALT="$W=\{1, 2, \ldots, n\}$">|;
$key = q/framebox{minipage{{.85textwidth}{smalltabbing{quad=quad=quad=quad[-1mm]{v_1=v{;[{>{y_l=y_l+r_l{textbf{endfor}[1mm]{w=y_1{;tabbing{}minipage{};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="430" HEIGHT="435" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img66.png"
ALT="\framebox{
\begin{minipage}{.85\textwidth} {\small
\begin{tabbing}
\quad \=\quad...
...= y_l+r_l$\\\\
\textbf{endfor} [1mm]
$w = y_1$;
\end{tabbing}}
\end{minipage}}">|;
$key = q/A;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="18" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img2.png"
ALT="$A$">|;
$key = q/i=1,ldots,m;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="97" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img30.png"
ALT="$i=1,\ldots,m$">|;
$key = q/y=op(M^{-1}),x;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="117" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img93.png"
ALT="$y = op(M^{-1}) x$">|;
$key = q/{displaymath}S=I-omegaD^{-1}A,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="126" HEIGHT="30" BORDER="0"
SRC="|."$dir".q|img83.png"
ALT="\begin{displaymath}
S = I - \omega D^{-1} A ,
\end{displaymath}">|;
$key = q/SinRe^{ntimesn};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="78" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img80.png"
ALT="$S \in \Re^{n \times n}$">|;
$key = q/theta;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="13" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img91.png"
ALT="$\theta$">|;
$key = q/{displaymath}M_{ASH}^{-1}=sum_{i=1}^m(R_i^{delta})^T(A_i^delta)^{-1}tilde{R}_i^0.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="218" HEIGHT="58" BORDER="0"
SRC="|."$dir".q|img41.png"
ALT="\begin{displaymath}M_{ASH}^{-1}= \sum_{i=1}^m (R_i^{\delta})^T
(A_i^\delta)^{-1} \tilde{R}_i^0.
\end{displaymath}">|;
$key = q/op(M^{-1})=M^{-C};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="136" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img100.png"
ALT="$op(M^{-1}) = M^{-C}$">|;
$key = q/W_i^deltasupsetW_i^{delta-1};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="97" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img14.png"
ALT="$W_i^\delta \supset W_i^{\delta-1}$">|;
$key = q/vinRe^n;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="56" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img19.png"
ALT="$v \in \Re^n$">|;
$key = q/W_i^deltabackslashW_i^0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="66" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img39.png"
ALT="$W_i^\delta \backslash W_i^0$">|;
$key = q/m;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="20" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img11.png"
ALT="$m$">|;
$key = q/{displaymath}P=(p_{ij}),quadp_{ij}=left{array{{ll}1&quadmbox{if};iinV^j_C0&quadmbox{otherwise}array{right..{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="290" HEIGHT="52" BORDER="0"
SRC="|."$dir".q|img77.png"
ALT="\begin{displaymath}
P=(p_{ij}), \quad p_{ij}=
\left\{ \begin{array}{ll}
1 &amp; \qu...
...\in V^j_C \\\\
0 &amp; \quad \mbox{otherwise}
\end{array} \right. .
\end{displaymath}">|;
1;
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