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\end{equation*}
where $\MI$ is the maximum number of outer iterations and $\epsilon$ is the
tolerance threshold of the error computed between two successive local solution
-$X_\ell^k$ and $X_\ell^{k+1}$.
+$X_\ell^k$ and $X_\ell^{k+1}$. It should be noted that with asynchronous iterative algorithms, we cannot use a classical norm (which would require to synchronize all processors), such as $\|X_\ell^k - X_\ell^{k+1}\|_{2}$ for example. Nevertheless, in our experiments, we check that the final result is correct, for this we compute the precision with $max_i | A*x-b |_i$.
increasing the matrix size up to $100^3$ elements, it was necessary to increase the
CPU power by \np[\%]{50} to \np[GFlops]{1.5} to get the algorithm convergence and the same order of asynchronous mode efficiency. Maintaining a relative gain of $2.5$ and such processor power but increasing network throughput inter cluster up to \np[Mbit/s]{50}, is obtained with
high external precision of \np{E-11} for a matrix size from $110^3$ to $150^3$ side
-elements.
+elements.
%For the 3 clusters architecture including a total of 100 hosts,
%Table~\ref{tab.cluster.3x33} shows that it was difficult to have a combination
