DL : expé encore

[rce2015.git] / paper.tex

diff --git a/paper.tex b/paper.tex
index 2c9b309bc9661048b70b46078c0ea028777afef9..0dc584b97e06d275b6cdd04c19ef1caf27b56aeb 100644 (file)
--- a/paper.tex
+++ b/paper.tex
@@ -45,6 +45,8 @@
   \todo[color=blue!10,#1]{\sffamily\textbf{LZK:} #2}\xspace}
 \newcommand{\RCE}[2][inline]{%
   \todo[color=yellow!10,#1]{\sffamily\textbf{RCE:} #2}\xspace}
   \todo[color=blue!10,#1]{\sffamily\textbf{LZK:} #2}\xspace}
 \newcommand{\RCE}[2][inline]{%
   \todo[color=yellow!10,#1]{\sffamily\textbf{RCE:} #2}\xspace}

+\newcommand{\DL}[2][inline]{%
+    \todo[color=pink!10,#1]{\sffamily\textbf{DL:} #2}\xspace}

 
 \algnewcommand\algorithmicinput{\textbf{Input:}}
 \algnewcommand\Input{\item[\algorithmicinput]}
 
 \algnewcommand\algorithmicinput{\textbf{Input:}}
 \algnewcommand\Input{\item[\algorithmicinput]}


@@ -96,20 +98,21 @@ performed. With some applications, it is difficult, if not impossible, to build
 accurate performance models. That is why another solution is to use a simulation
 tool which allows us to change many parameters of the architecture (network
 bandwidth, latency, number of processors) and to simulate the execution of such
 accurate performance models. That is why another solution is to use a simulation
 tool which allows us to change many parameters of the architecture (network
 bandwidth, latency, number of processors) and to simulate the execution of such

-applications. We have decided to use SimGrid as it enables to benchmark MPI
-applications.
+applications. The main contribution of this paper is to show that the use of a
+simulation tool (here we have decided to use the SimGrid toolkit) can really
+help developpers to better tune their applications for a given multi-core
+architecture.

 
 

-In this paper, we focus our attention on two parallel iterative algorithms based
+In particular we focus our attention on two parallel iterative algorithms based

 on the  Multisplitting algorithm  and we  compare them  to the  GMRES algorithm.
 on the  Multisplitting algorithm  and we  compare them  to the  GMRES algorithm.

-These algorithms  are used to  solve libear  systems. Two different  variants of
+These algorithms  are used to  solve linear  systems. Two different  variants of

 the Multisplitting are studied: one  using synchronoous  iterations and  another
 the Multisplitting are studied: one  using synchronoous  iterations and  another

-one  with asynchronous iterations. For each algorithm we have  tested different
-parameters to see their influence.  We strongly  recommend people  interested
-by investing  into a  new expensive  hardware  architecture  to   benchmark
-their  applications  using  a simulation tool before.
-
-
-
+one  with asynchronous iterations. For each algorithm we have simulated
+different architecture parameters to evaluate their influence on the overall
+execution time.  The obtain simulated results confirm the real results
+previously obtained on different real multi-core architectures and also confirm
+the efficiency of the asynchronous multisplitting algorithm compared to the
+synchronous GMRES method.

 
 \end{abstract}
 
 
 \end{abstract}
 


@@ -464,19 +467,19 @@ and  between distant  clusters.  This parameter is application dependent.
 
 In the scope  of this paper, our  first objective is to analyze  when the Krylov
 Multisplitting  method   has  better  performances  than   the  classical  GMRES
 
 In the scope  of this paper, our  first objective is to analyze  when the Krylov
 Multisplitting  method   has  better  performances  than   the  classical  GMRES

-method. With an  iterative method, better performances mean a  smaller number of
-iterations and execution time before reaching the convergence.  For a systematic
-study,  the experiments  should figure  out  that, for  various grid  parameters
-values, the simulator will confirm  the targeted outcomes, particularly for poor
-and slow  networks, focusing on the  impact on the communication  performance on
-the chosen class of algorithm.
+method. With a synchronous  iterative method, better performances mean a
+smaller number of iterations and execution time before reaching the convergence.
+For a systematic study,  the experiments  should figure  out  that, for  various
+grid  parameters values, the simulator will confirm  the targeted outcomes,
+particularly for poor and slow  networks, focusing on the  impact on the
+communication  performance on the chosen class of algorithm.

 
 The following paragraphs present the test conditions, the output results
 and our comments.\\
 
 
 
 The following paragraphs present the test conditions, the output results
 and our comments.\\
 
 

-\subsubsection{Execution of the the algorithms on various computational grid
-architecture and scaling up the input matrix size}
+\subsubsection{Execution of the algorithms on various computational grid
+architectures and scaling up the input matrix size}

 \ \\
 % environment
 
 \ \\
 % environment
 


@@ -500,9 +503,9 @@ architecture and scaling up the input matrix size}
 
 
 In this  section, we analyze the  performences of algorithms running  on various
 
 
 In this  section, we analyze the  performences of algorithms running  on various

-grid configuration  (2x16, 4x8, 4x16  and 8x8). First,  the results in  Figure~\ref{fig:01}
-show for all grid configuration the non-variation of the number of iterations of
-classical  GMRES for  a given  input matrix  size; it  is not  the case  for the
+grid configurations  (2x16, 4x8, 4x16  and 8x8). First,  the results in  Figure~\ref{fig:01}
+show for all grid configurations the non-variation of the number of iterations of
+classical  GMRES for  a given  input matrix  size; it is not  the case  for the

 multisplitting method.
 
 \RC{CE attention tu n'as pas mis de label dans tes figures, donc c'est le bordel, j'en mets mais vérifie...}
 multisplitting method.
 
 \RC{CE attention tu n'as pas mis de label dans tes figures, donc c'est le bordel, j'en mets mais vérifie...}


@@ -518,26 +521,28 @@ multisplitting method.
 \end{figure}
 
 
 \end{figure}
 
 

-The execution time difference between the two algorithms is important when
-comparing between different grid architectures, even with the same number of
-processors (like 2x16 and 4x8 = 32 processors for example). The
-experiment concludes the low sensitivity of the multisplitting method
-(compared with the classical GMRES) when scaling up the number of the processors in the grid: in average, the GMRES (resp. Multisplitting) algorithm performs 40\% better (resp. 48\%) less when running from 2x16=32 to 8x8=64 processors.
+The execution  times between  the two algorithms  is significant  with different
+grid architectures, even  with the same number of processors  (for example, 2x16
+and  4x8). We  can  observ  the low  sensitivity  of  the Krylov multisplitting  method
+(compared with the classical GMRES) when scaling up the number of the processors
+in the  grid: in  average, the GMRES  (resp. Multisplitting)  algorithm performs
+$40\%$ better (resp. $48\%$) when running from 2x16=32 to 8x8=64 processors.

 
 

-\textit{\\3.b Running on two different speed cluster inter-networks\\}
+\subsubsection{Running on two different inter-clusters network speed}
+\ \\

 
 

-% environment
-\begin{footnotesize}
+\begin{figure} [ht!]
+\begin{center}

 \begin{tabular}{r c }
  \hline
  Grid & 2x16, 4x8\\ %\hline
  Network & N1 : bw=10Gbs-lat=8.10$^{-6}$ \\ %\hline
  - & N2 : bw=1Gbs-lat=5.10$^{-5}$ \\
 \begin{tabular}{r c }
  \hline
  Grid & 2x16, 4x8\\ %\hline
  Network & N1 : bw=10Gbs-lat=8.10$^{-6}$ \\ %\hline
  - & N2 : bw=1Gbs-lat=5.10$^{-5}$ \\

- Input matrix size & N$_{x}$ x N$_{y}$ x N$_{z}$ =150 x 150 x 150\\ \hline \\
+ Input matrix size & N$_{x}$ x N$_{y}$ x N$_{z}$ =150 x 150 x 150\\ \hline

  \end{tabular}
  \end{tabular}

-Table 2 : Clusters x Nodes - Networks N1 x N2 \\
-
- \end{footnotesize}
+\caption{Clusters x Nodes - Networks N1 x N2}
+\end{center}
+\end{figure}

 
 
 
 
 
 


@@ -546,174 +551,175 @@ Table 2 : Clusters x Nodes - Networks N1 x N2 \\
 \centering
 \includegraphics[width=100mm]{cluster_x_nodes_n1_x_n2.pdf}
 \caption{Cluster x Nodes N1 x N2}
 \centering
 \includegraphics[width=100mm]{cluster_x_nodes_n1_x_n2.pdf}
 \caption{Cluster x Nodes N1 x N2}

-%\label{overflow}}
+\label{fig:02}

 \end{figure}
 %\end{wrapfigure}
 
 \end{figure}
 %\end{wrapfigure}
 

-The experiments compare the behavior of the algorithms running first on
-a speed inter- cluster network (N1) and also on a less performant network (N2).
-Figure 4 shows that end users will gain to reduce the execution time
-for both algorithms in using a grid architecture like 4x16 or 8x8: the
-performance was increased in a factor of 2. The results depict also that
-when the network speed drops down (12.5\%), the difference between the execution
-times can reach more than 25\%.
-
-\textit{\\3.c Network latency impacts on performance\\}
+These experiments  compare the  behavior of  the algorithms  running first  on a
+speed inter-cluster  network (N1) and  also on  a less performant  network (N2).
+Figure~\ref{fig:02} shows that end users will  gain to reduce the execution time
+for  both  algorithms  in using  a  grid  architecture  like  4x16 or  8x8:  the
+performance was increased  by a factor of  $2$. The results depict  also that when
+the  network speed  drops down  (12.5\%), the  difference between  the execution
+times can reach more than 25\%. \RC{c'est pas clair : la différence entre quoi et quoi?}
+\DL{pas clair}

 
 

-% environment
-\begin{footnotesize}
+\subsubsection{Network latency impacts on performance}
+\ \\
+\begin{figure} [ht!]
+\centering

 \begin{tabular}{r c }
  \hline
  Grid & 2x16\\ %\hline
  Network & N1 : bw=1Gbs \\ %\hline
 \begin{tabular}{r c }
  \hline
  Grid & 2x16\\ %\hline
  Network & N1 : bw=1Gbs \\ %\hline

- Input matrix size & N$_{x}$ x N$_{y}$ x N$_{z}$ =150 x 150 x 150\\ \hline\\
+ Input matrix size & N$_{x}$ x N$_{y}$ x N$_{z}$ =150 x 150 x 150\\ \hline

  \end{tabular}
  \end{tabular}

-Table 3 : Network latency impact \\
-
-\end{footnotesize}
+\caption{Network latency impacts}
+\end{figure}

 
 
 
 \begin{figure} [ht!]
 \centering
 \includegraphics[width=100mm]{network_latency_impact_on_execution_time.pdf}
 
 
 
 \begin{figure} [ht!]
 \centering
 \includegraphics[width=100mm]{network_latency_impact_on_execution_time.pdf}

-\caption{Network latency impact on execution time}
-%\label{overflow}}
+\caption{Network latency impacts on execution time}
+\label{fig:03}

 \end{figure}
 
 
 \end{figure}
 
 

-According the results in figure 5, degradation of the network
-latency from 8.10$^{-6}$ to 6.10$^{-5}$ implies an absolute time
-increase more than 75\% (resp. 82\%) of the execution for the classical
-GMRES (resp. multisplitting) algorithm. In addition, it appears that the
-multisplitting method tolerates more the network latency variation with
-a less rate increase of the execution time. Consequently, in the worst case (lat=6.10$^{-5
-}$), the execution time for GMRES is almost the double of the time for
-the multisplitting, even though, the performance was on the same order
-of magnitude with a latency of 8.10$^{-6}$.
-
-\textit{\\3.d Network bandwidth impacts on performance\\}
+According to the results  of  Figure~\ref{fig:03}, a  degradation  of the  network
+latency from $8.10^{-6}$  to $6.10^{-5}$ implies an absolute  time increase of more
+than $75\%$  (resp. $82\%$) of the  execution for the classical  GMRES (resp. Krylov
+multisplitting)   algorithm.   In   addition,   it  appears   that  the   Krylov
+multisplitting method tolerates  more the network latency variation  with a less
+rate  increase  of  the  execution   time.   Consequently,  in  the  worst  case
+($lat=6.10^{-5 }$), the  execution time for GMRES is almost  the double than the
+time of the Krylov multisplitting, even  though, the performance was on the same
+order of magnitude with a latency of $8.10^{-6}$.

 
 

-% environment
-\begin{footnotesize}
+\subsubsection{Network bandwidth impacts on performance}
+\ \\
+\begin{figure} [ht!]
+\centering

 \begin{tabular}{r c }
  \hline
  Grid & 2x16\\ %\hline
  Network & N1 : bw=1Gbs - lat=5.10$^{-5}$ \\ %\hline
  Input matrix size & N$_{x}$ x N$_{y}$ x N$_{z}$ =150 x 150 x 150\\ \hline \\
  \end{tabular}
 \begin{tabular}{r c }
  \hline
  Grid & 2x16\\ %\hline
  Network & N1 : bw=1Gbs - lat=5.10$^{-5}$ \\ %\hline
  Input matrix size & N$_{x}$ x N$_{y}$ x N$_{z}$ =150 x 150 x 150\\ \hline \\
  \end{tabular}

-Table 4 : Network bandwidth impact \\
-
-\end{footnotesize}
+\caption{Network bandwidth impacts}
+\end{figure}

 
 
 \begin{figure} [ht!]
 \centering
 \includegraphics[width=100mm]{network_bandwith_impact_on_execution_time.pdf}
 
 
 \begin{figure} [ht!]
 \centering
 \includegraphics[width=100mm]{network_bandwith_impact_on_execution_time.pdf}

-\caption{Network bandwith impact on execution time}
-%\label{overflow}
+\caption{Network bandwith impacts on execution time}
+\label{fig:04}

 \end{figure}
 
 \end{figure}
 

+The results  of increasing  the network  bandwidth show  the improvement  of the
+performance  for   both  algorithms   by  reducing   the  execution   time  (see
+Figure~\ref{fig:04}). However,  in this  case, the Krylov  multisplitting method
+presents a better  performance in the considered bandwidth interval  with a gain
+of $40\%$ which is only around $24\%$ for the classical GMRES.

 
 

-
-The results of increasing the network bandwidth show the improvement
-of the performance for both of the two algorithms by reducing the execution time (Figure 6). However, and again in this case, the multisplitting method presents a better performance in the considered bandwidth interval with a gain of 40\% which is only around 24\% for classical GMRES.
-
-\textit{\\3.e Input matrix size impacts on performance\\}
-
-% environment
-\begin{footnotesize}
+\subsubsection{Input matrix size impacts on performance}
+\ \\
+\begin{figure} [ht!]
+\centering

 \begin{tabular}{r c }
  \hline
  Grid & 4x8\\ %\hline
 \begin{tabular}{r c }
  \hline
  Grid & 4x8\\ %\hline

- Network & N2 : bw=1Gbs - lat=5.10$^{-5}$ \\ %\hline
- Input matrix size & N$_{x}$ = From 40 to 200\\ \hline \\
+ Network & N2 : bw=1Gbs - lat=5.10$^{-5}$ \\
+ Input matrix size & N$_{x}$ = From 40 to 200\\ \hline

  \end{tabular}
  \end{tabular}

-Table 5 : Input matrix size impact\\
-
-\end{footnotesize}
+\caption{Input matrix size impacts}
+\end{figure}

 
 
 \begin{figure} [ht!]
 \centering
 \includegraphics[width=100mm]{pb_size_impact_on_execution_time.pdf}
 
 
 \begin{figure} [ht!]
 \centering
 \includegraphics[width=100mm]{pb_size_impact_on_execution_time.pdf}

-\caption{Pb size impact on execution time}
-%\label{overflow}}
+\caption{Problem size impacts on execution time}
+\label{fig:05}

 \end{figure}
 
 \end{figure}
 

-In this experimentation, the input matrix size has been set from
-N$_{x}$ = N$_{y}$ = N$_{z}$ = 40 to 200 side elements that is from 40$^{3}$ = 64.000 to
-200$^{3}$ = 8.000.000 points. Obviously, as shown in the figure 7,
-the execution time for the two algorithms convergence increases with the
-iinput matrix size. But the interesting results here direct on (i) the
-drastic increase (300 times) of the number of iterations needed before
-the convergence for the classical GMRES algorithm when the matrix size
-go beyond N$_{x}$=150; (ii) the classical GMRES execution time also almost
-the double from N$_{x}$=140 compared with the convergence time of the
-multisplitting method. These findings may help a lot end users to setup
-the best and the optimal targeted environment for the application
-deployment when focusing on the problem size scale up. Note that the
-same test has been done with the grid 2x16 getting the same conclusion.
-
-\textit{\\3.f CPU Power impact on performance\\}
+In these experiments, the input matrix size  has been set from $N_{x} = N_{y}
+= N_{z} = 40$ to $200$ side elements  that is from $40^{3} = 64.000$ to $200^{3}
+= 8,000,000$  points. Obviously, as  shown in Figure~\ref{fig:05},  the execution
+time for  both algorithms increases when  the input matrix size  also increases.
+But the interesting results are:
+\begin{enumerate}
+  \item the drastic increase ($300$ times) \RC{Je ne vois pas cela sur la figure}
+of the  number of  iterations needed  to reach the  convergence for  the classical
+GMRES algorithm when  the matrix size go beyond $N_{x}=150$;
+\item the  classical GMRES execution time  is almost the double  for $N_{x}=140$
+  compared with the Krylov multisplitting method.
+\end{enumerate}

 
 

-% environment
-\begin{footnotesize}
+These  findings may  help a  lot end  users to  setup the  best and  the optimal
+targeted environment for the application deployment when focusing on the problem
+size scale up.  It  should be noticed that the same test has  been done with the
+grid 2x16 leading to the same conclusion.
+
+\subsubsection{CPU Power impacts on performance}
+
+\begin{figure} [ht!]
+\centering

 \begin{tabular}{r c }
  \hline
  Grid & 2x16\\ %\hline
  Network & N2 : bw=1Gbs - lat=5.10$^{-5}$ \\ %\hline
  Input matrix size & N$_{x}$ = 150 x 150 x 150\\ \hline
  \end{tabular}
 \begin{tabular}{r c }
  \hline
  Grid & 2x16\\ %\hline
  Network & N2 : bw=1Gbs - lat=5.10$^{-5}$ \\ %\hline
  Input matrix size & N$_{x}$ = 150 x 150 x 150\\ \hline
  \end{tabular}

-Table 6 : CPU Power impact \\
-
-\end{footnotesize}
-
+\caption{CPU Power impacts}
+\end{figure}

 
 \begin{figure} [ht!]
 \centering
 \includegraphics[width=100mm]{cpu_power_impact_on_execution_time.pdf}
 
 \begin{figure} [ht!]
 \centering
 \includegraphics[width=100mm]{cpu_power_impact_on_execution_time.pdf}

-\caption{CPU Power impact on execution time}
-%\label{overflow}}
-s\end{figure}
-
-Using the Simgrid simulator flexibility, we have tried to determine the
-impact on the algorithms performance in varying the CPU power of the
-clusters nodes from 1 to 19 GFlops. The outputs depicted in the figure 6
-confirm the performance gain, around 95\% for both of the two methods,
-after adding more powerful CPU.
-
-\subsection{Comparing GMRES in native synchronous mode and
-Multisplitting algorithms in asynchronous mode}
-
-The previous paragraphs put in evidence the interests to simulate the
-behavior of the application before any deployment in a real environment.
-We have focused the study on analyzing the performance in varying the
-key factors impacting the results. The study compares
-the performance of the two proposed algorithms both in \textit{synchronous mode
-}. In this section, following the same previous methodology, the goal is to
-demonstrate the efficiency of the multisplitting method in \textit{
-asynchronous mode} compared with the classical GMRES staying in
-\textit{synchronous mode}.
-
-Note that the interest of using the asynchronous mode for data exchange
-is mainly, in opposite of the synchronous mode, the non-wait aspects of
-the current computation after a communication operation like sending
-some data between nodes. Each processor can continue their local
-calculation without waiting for the end of the communication. Thus, the
-asynchronous may theoretically reduce the overall execution time and can
-improve the algorithm performance.
-
-As stated supra, Simgrid simulator tool has been used to prove the
-efficiency of the multisplitting in asynchronous mode and to find the
-best combination of the grid resources (CPU, Network, input matrix size,
-\ldots ) to get the highest \textit{"relative gain"} (exec\_time$_{GMRES}$ / exec\_time$_{multisplitting}$) in comparison with the classical GMRES time.
+\caption{CPU Power impacts on execution time}
+\label{fig:06}
+\end{figure}
+
+Using the Simgrid  simulator flexibility, we have tried to  determine the impact
+on the  algorithms performance in  varying the CPU  power of the  clusters nodes
+from $1$ to $19$ GFlops.  The outputs  depicted in Figure~\ref{fig:06}  confirm the
+performance gain,  around $95\%$ for  both of the  two methods, after  adding more
+powerful CPU.
+
+\DL{il faut une conclusion sur ces tests : ils confirment les résultats déjà
+obtenus en grandeur réelle. Donc c'est une aide précieuse pour les dev. Pas
+besoin de déployer sur une archi réelle}
+
+\subsection{Comparing GMRES in native synchronous mode and the multisplitting algorithm in asynchronous mode}
+
+The previous paragraphs  put in evidence the interests to  simulate the behavior
+of  the application  before  any  deployment in  a  real  environment.  In  this
+section, following  the same previous  methodology, our  goal is to  compare the
+efficiency of the multisplitting method  in \textit{ asynchronous mode} with the
+classical GMRES in \textit{synchronous mode}.
+
+The  interest of  using  an asynchronous  algorithm  is that  there  is no  more
+synchronization. With  geographically distant  clusters, this may  be essential.
+In  this case,  each  processor can  compute its  iteration  freely without  any
+synchronization  with   the  other   processors.  Thus,  the   asynchronous  may
+theoretically reduce  the overall execution  time and can improve  the algorithm
+performance.
+
+\RC{la phrase suivante est bizarre, je ne comprends pas pourquoi elle vient ici}
+As stated before, the Simgrid simulator tool has been successfully used to show
+the efficiency of  the multisplitting in asynchronous mode and  to find the best
+combination of the grid resources (CPU,  Network, input matrix size, \ldots ) to
+get    the   highest    \textit{"relative    gain"}   (exec\_time$_{GMRES}$    /
+exec\_time$_{multisplitting}$) in comparison with the classical GMRES time.

 
 
 The test conditions are summarized in the table below : \\
 
 
 
 The test conditions are summarized in the table below : \\
 

-% environment
-\begin{footnotesize}
+\begin{figure} [ht!]
+\centering

 \begin{tabular}{r c }
  \hline
  Grid & 2x50 totaling 100 processors\\ %\hline
 \begin{tabular}{r c }
  \hline
  Grid & 2x50 totaling 100 processors\\ %\hline


@@ -723,15 +729,17 @@ The test conditions are summarized in the table below : \\
  Input matrix size & N$_{x}$ = From 62 to 150\\ %\hline
  Residual error precision & 10$^{-5}$ to 10$^{-9}$\\ \hline \\
  \end{tabular}
  Input matrix size & N$_{x}$ = From 62 to 150\\ %\hline
  Residual error precision & 10$^{-5}$ to 10$^{-9}$\\ \hline \\
  \end{tabular}

-\end{footnotesize}
+\end{figure}

 
 

-Again, comprehensive and extensive tests have been conducted varying the
-CPU power and the network parameters (bandwidth and latency) in the
-simulator tool with different problem size. The relative gains greater
-than 1 between the two algorithms have been captured after each step of
-the test. Table 7 below has recorded the best grid configurations
-allowing the multisplitting method execution time more performant 2.5 times than
-the classical GMRES execution and convergence time. The experimentation has demonstrated the relative multisplitting algorithm tolerance when using a low speed network that we encounter usually with distant clusters thru the internet.
+Again,  comprehensive and  extensive tests  have been  conducted with  different
+parametes as  the CPU power, the  network parameters (bandwidth and  latency) in
+the simulator tool  and with different problem size. The  relative gains greater
+than 1  between the  two algorithms have  been captured after  each step  of the
+test.   In  Figure~\ref{table:01}  are  reported the  best  grid  configurations
+allowing the  multisplitting method to  be more than  2.5 times faster  than the
+classical  GMRES.  These  experiments also  show the  relative tolerance  of the
+multisplitting algorithm when using a low speed network as usually observed with
+geographically distant clusters throuth the internet.

 
 % use the same column width for the following three tables
 \newlength{\mytablew}\settowidth{\mytablew}{\footnotesize\np{E-11}}
 
 % use the same column width for the following three tables
 \newlength{\mytablew}\settowidth{\mytablew}{\footnotesize\np{E-11}}


@@ -742,14 +750,12 @@ the classical GMRES execution and convergence time. The experimentation has demo
     \end{tabular}}
 
 
     \end{tabular}}
 
 

-\begin{table}[!t]
-  \centering
+\begin{figure}[!t]
+\centering
+%\begin{table}

 %  \caption{Relative gain of the multisplitting algorithm compared with the classical GMRES}
 %  \label{"Table 7"}
 %  \caption{Relative gain of the multisplitting algorithm compared with the classical GMRES}
 %  \label{"Table 7"}

-Table 7. Relative gain of the multisplitting algorithm compared with
-the classical GMRES \\
-
-  \begin{mytable}{11}
+ \begin{mytable}{11}

     \hline
     bandwidth (Mbit/s)
     & 5     & 5     & 5         & 5         & 5  & 50        & 50        & 50        & 50        & 50 \\
     \hline
     bandwidth (Mbit/s)
     & 5     & 5     & 5         & 5         & 5  & 50        & 50        & 50        & 50        & 50 \\


@@ -770,7 +776,11 @@ the classical GMRES \\
     & 2.52     & 2.55     & 2.52     & 2.57     & 2.54 & 2.53     & 2.51     & 2.58     & 2.55     & 2.54 \\
     \hline
   \end{mytable}
     & 2.52     & 2.55     & 2.52     & 2.57     & 2.54 & 2.53     & 2.51     & 2.58     & 2.55     & 2.54 \\
     \hline
   \end{mytable}

-\end{table}
+%\end{table}
+ \caption{Relative gain of the multisplitting algorithm compared with the classical GMRES}
+ \label{table:01}
+\end{figure}
+

 
 \section{Conclusion}
 CONCLUSION
 
 \section{Conclusion}
 CONCLUSION