Relecture

[GMRES2stage.git] / paper.tex

diff --git a/paper.tex b/paper.tex
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--- a/paper.tex
+++ b/paper.tex
@@ -621,10 +621,11 @@ outer solver periodically applies a least-squares minimization  on the residuals
 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 
 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
 
 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