X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/GMRES2stage.git/blobdiff_plain/3aa4a4a5934c50b8ee7ac223ae1ebc31796c820c..61de3472de119515c917449ea4aea0a3240c8cb0:/paper.tex

diff --git a/paper.tex b/paper.tex
index 2372b61..4cd16c3 100644
--- a/paper.tex
+++ b/paper.tex
@@ -626,8 +626,8 @@ inner solver. The current approximation of the Krylov method is then stored insi
 $S$ composed by the successive solutions that are computed during inner iterations.
 
 At each $s$ iterations, the minimization step is applied in order to
-compute a new  solution $x$. For that, the previous  residuals are computed with
-$(b-AS)$. The minimization of the residuals is obtained by 
+compute a new  solution $x$. For that, the previous  residuals of $Ax=b$ are computed by
+the inner iterations with $(b-AS)$. The minimization of the residuals is obtained by  
 \begin{equation}
    \underset{\alpha\in\mathbb{R}^{s}}{min}\|b-R\alpha\|_2
 \label{eq:01}
@@ -654,7 +654,7 @@ appropriate than a single direct method in a parallel context.
     \State $S_{k \mod s}=x^k$ \label{algo:store}
     \If {$k \mod s=0$ {\bf and} error$>\epsilon_{kryl}$}
       \State $R=AS$ \Comment{compute dense matrix} \label{algo:matrix_mul}
-            \State Solve least-square problem $\underset{\alpha\in\mathbb{R}^{s}}{min}\|b-R\alpha\|_2$ \label{algo:}
+            \State $\alpha=Solve\_Least\_Squares(R,b,max\_iter_{ls})$ \label{algo:}
       \State $x^k=S\alpha$  \Comment{compute new solution}
     \EndIf
   \EndFor