\usepackage{algpseudocode}
\usepackage{amsmath}
\usepackage{amssymb}
+\usepackage{multirow}
\algnewcommand\algorithmicinput{\textbf{Input:}}
\algnewcommand\Input{\item[\algorithmicinput]}
In order to see the influence of our algorithm with only one processor, we first
show a comparison with the standard version of GMRES and our algorithm. In
table~\ref{tab:01}, we show the matrices we have used and some of them
-characteristics.
+characteristics. For all the matrices, the name, the field, the number of rows
+and the number of nonzero elements is given.
\begin{table}
\begin{center}
\end{center}
\end{table}
+In table~\ref{tab:02}, some experiments comparing the sovling of the linear
+systems obtained with the previous matrices with a GMRES variant and with out 2
+stage algorithm are given. In the second column, it can be noticed that either
+gmres or fgmres is used to solve the linear system. According to the matrices,
+different preconditioner is used. With the 2 stage algorithm, the same
+solver and the same preconditionner is used.
+\begin{table}
+\begin{center}
+\begin{tabular}{|c|c|r|r|r|r|}
+\hline
+
+ \multirow{2}{*}{Matrix name} & Solver / & \multicolumn{2}{c|}{gmres variant} & \multicolumn{2}{c|}{2 stage} \\
+ & precond & Time & \# Iter. & Time & \# Iter. \\\hline \hline
-%% \begin{table}
-%% \begin{center}
-%% \begin{tabular}{|c|c|r|r|r|}
-%% \hline
+crashbasis & gmres / none & 15.65 & 518 & 14.12 & 450 \\
+parabolic\_fem & gmres / ilu & 1009.94 & 7573 & 401.52 & 2970 \\
+epb3 & fgmres / sor & 8.67 & 600 & 8.21 & 540 \\
+atmosmodj & fgmres / sor & 104.23 & 451 & 88.97 & 366 \\
+bfwa398 & gmres / none & 1.42 & 9612 & 0.28 & 1650 \\
+torso3 & fgmres/sor & 565 & 37.70 & 34.97 & 510 \\
+\hline
-%% Matrix name & GMRES version &\# Rows & \# Nonzeros \\\hline \hline
+\end{tabular}
+\caption{Comparison of GMRES and 2 stage GMRES algorithms in sequential with some matrices, time is expressed in seconds.}
+\label{tab:02}
+\end{center}
+\end{table}
-%% crashbasis & GMRES & Optimization & 160,000 & 1,750,416 \\
-%% parabolic\_fem & & Computational fluid dynamics & 525,825 & 2,100,225 \\
-%% epb3 & & Thermal problem & 84,617 & 463,625 \\
-%% atmosmodj & Computational fluid dynamics & 1,270,432 & 8,814,880 \\
-%% bfwa398 & Electromagnetics problem & 398 & 3,678 \\
-%% torso3 & 2D/3D problem & 259,156 & 4,429,042 \\
-%% \hline
-%% \end{tabular}
-%% \caption{Comparison of GMRES and 2 stage GMRES algorithms in sequential with some matrices}
-%% \label{tab:01}
-%% \end{center}
-%% \end{table}
+Param : retart 30 iters
+cols = 8
+iter cgls = 20
+cgls prec = 1e-40
+prec = 1e-10
+Intel(R) Core(TM) i7-3630QM CPU @ 2.40GHz
%%%*********************************************************
