new

[book_gpu.git] / BookGPU / Chapters / chapter12 / ch12.tex

diff --git a/BookGPU/Chapters/chapter12/ch12.tex b/BookGPU/Chapters/chapter12/ch12.tex
index 4fe0eb97b97f30755ed469d87a43ee7b2a94bcbd..5c0a5b2302b3adcd5086daa1d49126b7515da756 100755 (executable)
--- a/BookGPU/Chapters/chapter12/ch12.tex
+++ b/BookGPU/Chapters/chapter12/ch12.tex
@@ -548,8 +548,10 @@ which are the number of rows, the total number of nonzero values, and the maxima
 the present chapter, the bandwidth of a sparse matrix is defined as the number of matrix columns separating
 the first and the last nonzero value on a matrix row.
 
 the present chapter, the bandwidth of a sparse matrix is defined as the number of matrix columns separating
 the first and the last nonzero value on a matrix row.
 

+

 \begin{table}
 \centering
 \begin{table}
 \centering

+\begin{small}

 \begin{tabular}{|c|c|c|c|c|}
 \hline
 {\bf Matrix Type}             & {\bf Matrix Name} & {\bf \# Rows} & {\bf \# Nonzeros} & {\bf Bandwidth} \\ \hline \hline
 \begin{tabular}{|c|c|c|c|c|}
 \hline
 {\bf Matrix Type}             & {\bf Matrix Name} & {\bf \# Rows} & {\bf \# Nonzeros} & {\bf Bandwidth} \\ \hline \hline


@@ -578,10 +580,12 @@ the first and the last nonzero value on a matrix row.
 
                               & torso3            & $259,156$     & $4,429,042$  & $216,854$  \\ \hline
 \end{tabular}
 
                               & torso3            & $259,156$     & $4,429,042$  & $216,854$  \\ \hline
 \end{tabular}

+\end{small}

 \caption{Main characteristics of sparse matrices chosen from the University of Florida collection.}
 \label{ch12:tab:01}
 \end{table}
 
 \caption{Main characteristics of sparse matrices chosen from the University of Florida collection.}
 \label{ch12:tab:01}
 \end{table}
 

+

 \begin{table}[!h]
 \begin{center}
 \begin{tabular}{|c|c|c|c|c|c|c|} 
 \begin{table}[!h]
 \begin{center}
 \begin{tabular}{|c|c|c|c|c|c|c|} 


@@ -607,6 +611,7 @@ thermal2          & $1.172s$           & $0.622s$            & $1.88$        & $
 
 \begin{table}[!h]
 \begin{center}
 
 \begin{table}[!h]
 \begin{center}

+\begin{small}

 \begin{tabular}{|c|c|c|c|c|c|c|} 
 \hline
 {\bf Matrix}     & $\mathbf{Time_{cpu}}$ & $\mathbf{Time_{gpu}}$ & $\mathbf{\tau}$  & $\mathbf{\#~Iter.}$ & $\mathbf{Prec.}$     & $\mathbf{\Delta}$   \\ \hline \hline
 \begin{tabular}{|c|c|c|c|c|c|c|} 
 \hline
 {\bf Matrix}     & $\mathbf{Time_{cpu}}$ & $\mathbf{Time_{gpu}}$ & $\mathbf{\tau}$  & $\mathbf{\#~Iter.}$ & $\mathbf{Prec.}$     & $\mathbf{\Delta}$   \\ \hline \hline


@@ -635,6 +640,7 @@ poli\_large       & $0.097s$           & $0.095s$            & $1.02$        & $
 
 torso3            & $4.242s$           & $2.030s$            & $2.09$        & $175$          & $2.69e$-$10$     & $1.78e$-$14$ \\ \hline
 \end{tabular}
 
 torso3            & $4.242s$           & $2.030s$            & $2.09$        & $175$          & $2.69e$-$10$     & $1.78e$-$14$ \\ \hline
 \end{tabular}

+\end{small}

 \caption{Performances of the parallel GMRES method on a cluster 24 CPU cores vs. on cluster of 12 GPUs.}
 \label{ch12:tab:03}
 \end{center}
 \caption{Performances of the parallel GMRES method on a cluster 24 CPU cores vs. on cluster of 12 GPUs.}
 \label{ch12:tab:03}
 \end{center}


@@ -742,7 +748,7 @@ are better than those of the GMRES method for solving large symmetric linear sys
 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.
 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.

-
+\clearpage

 \begin{table}[!h]
 \begin{center}
 \begin{tabular}{|c|c|c|c|c|c|c|} 
 \begin{table}[!h]
 \begin{center}
 \begin{tabular}{|c|c|c|c|c|c|c|} 


@@ -769,6 +775,7 @@ on a cluster of 12 GPUs.}
 
 \begin{table}[!h]
 \begin{center}
 
 \begin{table}[!h]
 \begin{center}

+\begin{small}

 \begin{tabular}{|c|c|c|c|c|c|c|} 
 \hline
 {\bf Matrix}      & $\mathbf{Time_{cpu}}$ & $\mathbf{Time_{gpu}}$ & $\mathbf{\tau}$ & $\mathbf{\#~Iter.}$ & $\mathbf{Prec.}$ & $\mathbf{\Delta}$   \\ \hline \hline
 \begin{tabular}{|c|c|c|c|c|c|c|} 
 \hline
 {\bf Matrix}      & $\mathbf{Time_{cpu}}$ & $\mathbf{Time_{gpu}}$ & $\mathbf{\tau}$ & $\mathbf{\#~Iter.}$ & $\mathbf{Prec.}$ & $\mathbf{\Delta}$   \\ \hline \hline


@@ -797,6 +804,7 @@ poli\_large       & $8.515s$             & $1.053s$              & $8.09$
 
 torso3            & $31.463s$            & $3.681s$              & $8.55$          & $175$               & $2.69e$-$10$     & $2.66e$-$14$ \\ \hline
 \end{tabular}
 
 torso3            & $31.463s$            & $3.681s$              & $8.55$          & $175$               & $2.69e$-$10$     & $2.66e$-$14$ \\ \hline
 \end{tabular}

+\end{small}

 \caption{Performances of the parallel GMRES method for solving linear systems associated to sparse banded matrices on a cluster of 24 CPU cores vs. 
 on a cluster of 12 GPUs.}
 \label{ch12:tab:06}
 \caption{Performances of the parallel GMRES method for solving linear systems associated to sparse banded matrices on a cluster of 24 CPU cores vs. 
 on a cluster of 12 GPUs.}
 \label{ch12:tab:06}