X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/book_gpu.git/blobdiff_plain/b4a21f0b9226126a2c50f54a5518be5ef7c60749..cf0ee588a0ef05623f955938e81be1aa96c33f46:/BookGPU/Chapters/chapter12/ch12.tex diff --git a/BookGPU/Chapters/chapter12/ch12.tex b/BookGPU/Chapters/chapter12/ch12.tex index 4fe0eb9..5c0a5b2 100755 --- 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. + \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 @@ -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} +\end{small} \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|} @@ -607,6 +611,7 @@ thermal2 & $1.172s$ & $0.622s$ & $1.88$ & $ \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 @@ -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} +\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} @@ -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. - +\clearpage \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{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 @@ -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} +\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}