parallel algorithms called \texttt{numerical iterative algorithms} executed in a distributed environment. As their name
suggests, these algorithm solves a given problem by successive iterations ($X_{n +1} = f(X_{n})$) from an initial value
$X_{0}$ to find an approximate value $X^*$ of the solution with a very low residual error. Several well-known methods
-demonstrate the convergence of these algorithms \cite{}.
+demonstrate the convergence of these algorithms \cite{BT89,Bahi07}.
Parallelization of such algorithms generally involved the division of the problem into several \emph{blocks} that will
be solved in parallel on multiple processing units. The latter will communicate each intermediate results before a new
computations do not need to wait for required data. Processors can then perform their iterations with the data present
at that time. Even if the number of iterations required before the convergence is generally greater than for the
synchronous case, AIAC algorithms can significantly reduce overall execution times by suppressing idle times due to
-synchronizations especially in a grid computing context (see \cite{bcvc06:ij} for more details).
+synchronizations especially in a grid computing context (see \cite{Bahi07} for more details).
Parallel numerical applications (synchronous or asynchronous) may have different configuration and deployment
requirements. Quantifying their resource allocation policies and application scheduling algorithms in
grid computing environments under varying load, CPU power and network speeds is very costly, very labor intensive and very time
-consuming \cite{BuRaCa}. The case of AIAC algorithms is even more problematic since they are very sensible to the
+consuming \cite{Calheiros:2011:CTM:1951445.1951450}. The case of AIAC algorithms is even more problematic since they are very sensible to the
execution environment context. For instance, variations in the network bandwith (intra and inter- clusters), in the
number and the power of nodes, in the number of clusters... can lead to very different number of iterations and so to
very different execution times. Then, it appears that the use of simulation tools to explore various platform
As exposed in the introduction, parallel iterative methods are now widely used in many scientific domains. They can be
classified in three main classes depending on how iterations and communications are managed (for more details readers
-can refer to \cite{bcvc02:ip}). In the \textit{Synchronous Iterations - Synchronous Communications (SISC)} model data
+can refer to \cite{bcvc06:ij}). In the \textit{Synchronous Iterations - Synchronous Communications (SISC)} model data
are exchanged at the end of each iteration. All the processors must begin the same iteration at the same time and
important idle times on processors are generated. The \textit{Synchronous Iterations - Asynchronous Communications
(SIAC)} model can be compared to the previous one except that data required on another processor are sent asynchronously
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Simulation of the multisplitting method}
%Décrire le problème (algo) traité ainsi que le processus d'adaptation à SimGrid.
-Let $Ax=b$ be a large sparse system of $n$ linear equations in $\mathbb{R}$, where $A$ is a sparse square and nonsingular matrix, $x$ is the solution vector and $b$ is the right-hand side vector. We use a multisplitting method based on the block Jacobi splitting to solve this linear system on a large scale platform composed of $L$ clusters of processors. In this case, we apply a row-by-row splitting without overlapping
+Let $Ax=b$ be a large sparse system of $n$ linear equations in $\mathbb{R}$, where $A$ is a sparse square and nonsingular matrix, $x$ is the solution vector and $b$ is the right-hand side vector. We use a multisplitting method based on the block Jacobi splitting to solve this linear system on a large scale platform composed of $L$ clusters of processors~\cite{o1985multi}. In this case, we apply a row-by-row splitting without overlapping
\[
\left(\begin{array}{ccc}
A_{11} & \cdots & A_{1L} \\
\section*{Acknowledgment}
-
+This work is partially funded by the Labex ACTION program (contract ANR-11-LABX-01-01).
The authors would like to thank\dots{}
