$X_{0}$ 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
convergence depends on the delay of messages. With synchronous iterations, the
number of iterations is exactly the same than in the sequential mode (if the
parallelization process does not change the algorithm). So the difficulty with
-asynchronous iteratie algorithms comes from the fact it is necessary to run the algorithm
+asynchronous iterative algorithms comes from the fact it is necessary to run the algorithm
with real data. In fact, from an execution to another the order of messages will
change and the number of iterations to reach the convergence will also change.
According to all the parameters of the platform (number of nodes, power of
-nodes, inter and intra clusrters bandwith and latency, ....) and of the
+nodes, inter and intra clusrters bandwith and latency, etc.) and of the
algorithm (number of splitting with the multisplitting algorithm), the
multisplitting code will obtain the solution more or less quickly. Or course,
the GMRES method also depends of the same parameters. As it is difficult to have
