Asynchronous iterative methods have been studied for many years theoretically 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
-(i.e. problems for which the solution is $x^\star =f(x^\star)$. In practice,
+(i.e. problems for which the solution is $x^\star =f(x^\star)$). In practice,
asynchronous iteration methods can be used to solve, for example, linear and
non-linear systems of equations or optimization problems, interested readers are
invited to read~\cite{BT89,bahi07}.
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, iterations are synchronized whereas in the asynchronous
-one, they are not. It should be noticed that non-blocking communications can be
+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
architectures are often very important. So, prior to deployment and tests it
seems very promising to be able to simulate the behavior of asynchronous
iterative algorithms. The problematic is then to show that the results produced
-by simulation are in accordance with reality i.e. of the same order of
-magnitude. To our knowledge, there is no study on this problematic.
+by simulation are in accordance with reality (i.e. of the same order of
+magnitude). To our knowledge, there is no study on this problematic.
\section{SimGrid}
\label{sec:simgrid}
