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
+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 matrix
$S$ composed by the successive solutions that are computed during inner iterations.
