\section{The asynchronous iteration model}
\label{sec:asynchro}
-Asynchronous iterative methods have been studied for many years theorecally and
+Asynchronous iterative methods have been studied for many years theoritecally and
practically. Many methods have been considered and convergence results have been
-proved. These methods can be used to solve in parallel fixed point problems
+proved. These methods can be used to solve, in parallel, fixed point problems
(i.e. problems for which the solution is $x^\star =f(x^\star)$. In practice,
asynchronous iterations methods can be used to solve, for example, linear and
non-linear systems of equations or optimization problems, interested readers are
algorithm that supports both the synchronous or the asynchronous iteration model
requires very few modifications to be able to be executed in both variants. In
practice, only the communications and convergence detection are different. In
-the synchronous mode, the iterations are synchronized whereas in the
-asynchronous one, they are not. It should be noticed that non blocking
-communications can be used in both modes. Concerning the convergence detection,
-synchronous variants can use a global convergence procedure which acts as a
-global synchronization point. In the asynchronous model, the convergence dectection is more tricky as it must not synchronize all the processors. Interested readers can consult~\cite{myBCCV05c,bahi07,ccl09:ij}.
+the synchronous mode, iterations are synchronized whereas in the asynchronous
+one, they are not. It should be noticed that non blocking communications can be
+used in both modes. Concerning the convergence detection, synchronous variants
+can use a global convergence procedure which acts as a global synchronization
+point. In the asynchronous model, the convergence detection is more tricky as
+it must not synchronize all the processors. Interested readers can
+consult~\cite{myBCCV05c,bahi07,ccl09:ij}.
\section{SimGrid}
\label{sec:simgrid}
\section*{Acknowledgment}
-
-The authors would like to thank\dots{}
+This work is partially funded by the Labex ACTION program (contract ANR-11-LABX-01-01).
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