\batchmode
\documentclass[a4paper,twoside,11pt]{article}

\usepackage{pstricks}
\usepackage{fancybox}
\usepackage{amsfonts}
\usepackage{ifpdf}
\usepackage[bookmarks=true,             bookmarksnumbered=true,             bookmarksopen=false,             plainpages=false,            pdfpagelabels,            colorlinks,             linkcolor=blue]{hyperref}
\usepackage{ifthen}
\usepackage{graphicx}

\newtheorem{theorem}{Theorem} 
\newtheorem{corollary}{Corollary} \usepackage{rotating}


\pdfoutput=0



\setlength \textwidth{1.15\textwidth}
\pagestyle{myheadings}



\newcounter{subroutine}[subsection] 
\newcounter{example}[subroutine] \makeatletter%
\providecommand{\subsubroutine}[2]{%
\stepcounter{subroutine}%
      \subsection*{\flushleft #1---#2 \endflushleft}%
      \addcontentsline{toc}{subsubsection}{#1}%
      \markright{#1}}%%
\providecommand{\examplename}{Example}%
\providecommand{\syntaxname}{Syntax} 

\makeatother%
\providecommand{\example}{\stepcounter{example}%
\section*{Example~\arabic{example}}} 

%
\providecommand{\precdata}{\hyperlink{precdata}{{\tt mld\_prec\_type}}}%
\providecommand{\descdata}{\hyperlink{descdata}{{\tt psb\_desc\_type}}}%
\providecommand{\spdata}{\hyperlink{spdata}{{\tt psb\_spmat\_type}}}%
\providecommand{\Ref}[1]{\mbox{(\ref{#1})}} 



\usepackage[dvips]{pstcol}


\pagecolor[gray]{.7}

\usepackage[latin1]{inputenc}



\makeatletter

\makeatletter
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\newcommand\lthtmlinlineA{\bgroup\catcode`\_=8 \lthtmlinlineB}%
\newcommand\lthtmlinlineB[1]{\lthtmlmathtype{#1}\egroup\lthtmlhboxmathA}%
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\def\centerinlinemath{%
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\def\lthtmlcheckvsize{\ifdim\ht\sizebox<\vsize 
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\providecommand{\selectlanguage}[1]{}%
\makeatletter \tracingstats = 1 


\begin{document}
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\setcounter{page}{1}
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% !!! IMAGES START HERE !!!



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\begingroup 
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{\newpage\clearpage
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Ax=b, 
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{\newpage\clearpage
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$A$%
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{\newpage\clearpage
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$G=(W,E)$%
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{\newpage\clearpage
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$W=\{1, 2, \ldots, n\}$%
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{\newpage\clearpage
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$E=\{(i,j) : a_{ij} \neq 0\}$%
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{\newpage\clearpage
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$\delta$%
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{\newpage\clearpage
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$W$%
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{\newpage\clearpage
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$m$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline608}%
$W_i^0 \subset W$%
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$\cup_{i=1}^m W_i^0 = W$%
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{\newpage\clearpage
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$W_i^\delta \supset W_i^{\delta-1}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline618}%
$W_i^{\delta-1}$%
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{\newpage\clearpage
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$n_i^\delta$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline622}%
$W_i^\delta$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline624}%
$R_i^{\delta} \in 
\Re^{n_i^\delta \times n}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline626}%
$v \in \Re^n$%
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$v_i^{\delta} \in \Re^{n_i^\delta}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline630}%
$v$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline634}%
$R_i^{\delta}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline636}%
$\Re^{n_i^\delta}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline638}%
$\Re^n$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline640}%
$A_i^\delta=R_i^\delta A (R_i^\delta)^T \in
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{\newpage\clearpage
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$W_i^{\delta}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath564}%
\begin{displaymath}
M_{AS}^{-1}= \sum_{i=1}^m (R_i^{\delta})^T 
(A_i^\delta)^{-1} R_i^{\delta},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
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$A_i^\delta$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline652}%
$v_i = R_i^{\delta} v$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline654}%
$i=1,\ldots,m$%
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$A_i^\delta w_i = v_i$%
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$w_i$%
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$w = \sum_{i=1}^m (R_i^{\delta})^T w_i$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline664}%
$p$%
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$p,t$%
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{\newpage\clearpage
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\begin{displaymath}
M_{RAS}^{-1}= \sum_{i=1}^m (\tilde{R}_i^0)^T 
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\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath566}%
\begin{displaymath} M_{ASH}^{-1}= \sum_{i=1}^m (R_i^{\delta})^T 
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\end{displaymath}%
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$\delta=0$%
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{\newpage\clearpage
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$A_C$%
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{\newpage\clearpage
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$W_C$%
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A_C=R_C A R_C^T
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$M_{1L}$%
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M_{C}^{-1}= R_C^T A_C^{-1} R_C,
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M_{2LA}^{-1} = M_{C}^{-1} + M_{1L}^{-1}. 
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\begin{displaymath}
\begin{array}{l}
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\end{displaymath}%
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$M$%
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$w=M^{-1}v$%
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$nlev$%
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$l$%
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$A_l$%
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$A_1=A$%
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\quad \=\quad \=\quad \=\quad \\[-1mm]
$v_1 = v$; \\[2mm]
\textbf{for $l=2, nlev$\  do}\\[1mm]
\> ! transfer $v_{l-1}$\  to the next coarser level\\
\>  $v_l = R_lv_{l-1}$\  \\[1mm]
\textbf{endfor} \\[2mm]
! apply the coarsest-level correction\\[1mm]
$y_{nlev} = A_{nlev}^{-1} v_{nlev}$\\[2mm]
\textbf{for $l=nlev -1 , 1, -1$\  do}\\[1mm]
\> ! transfer $y_{l+1}$\  to the next finer level\\
\> $y_l = R_{l+1}^T y_{l+1}$;\\[1mm]
\> ! compute the residual at the current level\\
\> $r_l = v_l-A_l^{-1} y_l$;\\[1mm]
\> ! apply the basic Schwarz preconditioner to the residual\\
\> $r_l = M_l^{-1} r_l$\\[1mm]
\> ! update $y_l$\\
\> $y_l = y_l+r_l$\\
\textbf{endfor} \\[1mm]
$w = y_1$;
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{\newpage\clearpage
\lthtmldisplayA{displaymath574}%
\begin{displaymath}  N_r = \left\{s \in W: |a_{rs}| > \theta \sqrt{|a_{rr}a_{ss}|} \right\}
    \cup \left\{ r \right\} ,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline804}%
$\theta \in [0,1]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline806}%
$i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline808}%
$W_i^0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline812}%
$P_C=R_C^T$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline814}%
$P \in \Re^{n \times n_C}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath531}%
\begin{displaymath} 
P=(p_{ij}), \quad  p_{ij}= 
\left\{ \begin{array}{ll}
1 & \quad \mbox{if} \; i \in V^j_C \\
0 & \quad \mbox{otherwise}
\end{array} \right. .
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline816}%
$P_C$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline818}%
$P$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline820}%
$S \in \Re^{n \times n}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath542}%
\begin{displaymath}
P_C = S P,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline822}%
$S$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath546}%
\begin{displaymath}
S = I - \omega D^{-1} A , 
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline824}%
$\omega$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline826}%
$D^{-1}A$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline983}%
$\theta = 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1324}%
$w$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1328}%
$\ge 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1342}%
$t$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1346}%
$\in [0, 1]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1348}%
$\theta$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1352}%
$>0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1374}%
$y = op(M^{-1})\, x$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1378}%
$op$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1382}%
$x$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1384}%
$y$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1386}%
$op(M^{-1}) = M^{-1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1388}%
$op(M^{-1}) = M^{-T}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1390}%
$M^{-1})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1392}%
$op(M^{-1}) = M^{-C}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{section}
\appendix
\stepcounter{section}

\end{document}