all clusters are interconnected by a virtual unidirectional ring network (see
Figure~\ref{fig:4.1}). During the resolution, a Boolean token circulates around
the virtual ring from a master processor to another until the global convergence
-is achieved. So starting from the cluster with rank 1, each master processor $i$
+is achieved. So starting from the cluster with rank 1, each master processor $\ell$
sets the token to \textit{True} if the local convergence is achieved or to
-\textit{False} otherwise, and sends it to master processor $i+1$. Finally, the
+\textit{False} otherwise, and sends it to master processor $\ell+1$. Finally, the
global convergence is detected when the master of cluster 1 receives from the
master of cluster $L$ a token set to \textit{True}. In this case, the master of
cluster 1 broadcasts a stop message to masters of other clusters. In this work,
After analyzing the outputs, generally, for the two clusters including one hundred hosts configuration (Tables~\ref{tab.cluster.2x50}), some combinations of parameters affecting
the results have given a relative gain more than 2.5, showing the effectiveness of the
-asynchronous multiplsitting compared to GMRES with two distant clusters.
+asynchronous multisplitting compared to GMRES with two distant clusters.
With these settings, Table~\ref{tab.cluster.2x50} shows
that after setting the bandwidth of the inter cluster network to \np[Mbit/s]{5} and a latency in order of one hundredth of millisecond and a processor power
