of asynchronous iterative algorithms. For that, we compare the behaviour of a
synchronous GMRES algorithm with an asynchronous multisplitting one with
simulations which let us easily choose some parameters. Both codes are real MPI
-codes ans simulations allow us to see when the asynchronous multisplitting algorithm can be more
+codes and simulations allow us to see when the asynchronous multisplitting algorithm can be more
efficient than the GMRES one to solve a 3D Poisson problem.
$X_{0}$ 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{BT89,Bahi07}.
-Parallelization of such algorithms generally involve the division of the problem
+Parallelization of such algorithms generally involves 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 iteration starts and until the approximate solution is reached. These
\begin{figure}[!t]
\centering
- \includegraphics[width=60mm,keepaspectratio]{clustering2}
-\caption{Example of two distant clusters of processors.}
+ \includegraphics[width=60mm,keepaspectratio]{clustering}
+\caption{Example of three distant clusters of processors.}
\label{fig:4.1}
\end{figure}
