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+1%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%% CHAPTER 12 %%
%% %%
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%\chapterauthor{}{}
-\chapterauthor{Lilia Ziane Khodja}{Femto-ST Institute, University of Franche-Comte, France}
-\chapterauthor{Raphaël Couturier}{Femto-ST Institute, University of Franche-Comte, France}
-\chapterauthor{Jacques Bahi}{Femto-ST Institute, University of Franche-Comte, France}
+\chapterauthor{Lilia Ziane Khodja, Raphaël Couturier and Jacques Bahi}{Femto-ST Institute, University of Franche-Comte, France}
+%\chapterauthor{Raphaël Couturier}{Femto-ST Institute, University of Franche-Comte, France}
+%\chapterauthor{Jacques Bahi}{Femto-ST Institute, University of Franche-Comte, France}
-\chapter{Solving sparse linear systems with GMRES and CG methods on GPU clusters}
+\chapter[Solving linear systems with GMRES and CG methods on GPU clusters]{Solving sparse linear systems with GMRES and CG methods on GPU clusters}
\label{ch12}
%%--------------------------%%
diagonal are filled with sub-copies (left-copy and right-copy in Figure~\ref{ch12:fig:06}) of the same
initial matrix.
-\begin{figure}
+\begin{figure}[htbp]
\centerline{\includegraphics[scale=0.30]{Chapters/chapter12/figures/generation}}
\caption{Parallel generation of a large sparse matrix by four computing nodes.}
\label{ch12:fig:06}
\end{figure}
-\begin{table}[!h]
+\begin{table}[htbp]
\centering
\begin{tabular}{|c|c|c|c|}
\hline
\label{ch12:tab:04}
\end{table}
-We have used the parallel CG and GMRES algorithms for solving sparse linear systems of $25$
-million unknown values. The sparse matrices associated to these linear systems are generated
-from those presented in Table~\ref{ch12:tab:01}. Their main characteristics are given in Table~\ref{ch12:tab:04}.
-Tables~\ref{ch12:tab:05} and~\ref{ch12:tab:06} shows the performances of the parallel CG and
-GMRES solvers, respectively, obtained on a cluster of $24$ CPU cores and on a cluster of $12$
-GPUs. Obviously, we can notice from these tables that solving large sparse linear systems on
-a GPU cluster is more efficient than on a CPU cluster (see relative gains $\tau$). We can also
-notice that the execution times of the CG method, whether in a CPU cluster or in a GPU cluster,
-are better than those of the GMRES method for solving large symmetric linear systems. In fact, the
-CG method is characterized by a better convergence\index{Convergence} rate and a shorter execution
-time of an iteration than those of the GMRES method. Moreover, an iteration of the parallel GMRES
-method requires more data exchanges between computing nodes compared to the parallel CG method.
-
-\begin{table}
+\begin{table}[htbp]
\begin{center}
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
\end{center}
\end{table}
+
+We have used the parallel CG and GMRES algorithms for solving sparse linear systems of $25$
+million unknown values. The sparse matrices associated to these linear systems are generated
+from those presented in Table~\ref{ch12:tab:01}. Their main characteristics are given in Table~\ref{ch12:tab:04}.
+Tables~\ref{ch12:tab:05} and~\ref{ch12:tab:06} shows the performances of the parallel CG and
+GMRES solvers, respectively, obtained on a cluster of $24$ CPU cores and on a cluster of $12$
+GPUs. Obviously, we can notice from these tables that solving large sparse linear systems on
+a GPU cluster is more efficient than on a CPU cluster (see relative gains $\tau$). We can also
+notice that the execution times of the CG method, whether in a CPU cluster or in a GPU cluster,
+are better than those of the GMRES method for solving large symmetric linear systems. In fact, the
+CG method is characterized by a better convergence\index{Convergence} rate and a shorter execution
+time of an iteration than those of the GMRES method. Moreover, an iteration of the parallel GMRES
+method requires more data exchanges between computing nodes compared to the parallel CG method.
+
+
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%% SECTION 5 %%
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