At each outer iteration, the sparse linear system $Ax=b$ is partially
solved using only $m$
iterations of an iterative method, this latter being initialized with the
-best known approximation previously obtained.
-GMRES method~\cite{Saad86}, or any of its variants, can be used for instance as an
-inner solver. The current approximation of the Krylov method is then stored inside a matrix
-$S$ composed by the successive solutions that are computed during inner iterations.
+last obtained approximation.
+GMRES method~\cite{Saad86}, or any of its variants, can potentially be used as
+inner solver. The current approximation of the Krylov method is then stored inside a $n \times s$ matrix
+$S$, which is composed by the $s$ last solutions that have been computed during
+the inner iterations phase.
At each $s$ iterations, the minimization step is applied in order to
compute a new solution $x$. For that, the previous residuals of $Ax=b$ are computed by
