X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/GMRES2stage.git/blobdiff_plain/12080b70975c1166b9faba747f271766a8c8dd75..6fda575b88fae086f925cd4dcf960fc2af0d3b4f:/paper.tex

diff --git a/paper.tex b/paper.tex
index e540970..04ad634 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
@@ -940,7 +940,7 @@ the number of iterations. So, the overall benefit of using TSIRM is interesting.
 \end{table*}
 
 
-In Table~\ref{tab:04}, some experiments with example ex54 on the Curie architecture are reported
+In Table~\ref{tab:04}, some experiments with example ex54 on the Curie architecture are reported.
 
 
 \begin{table*}[htbp]
@@ -965,6 +965,13 @@ In Table~\ref{tab:04}, some experiments with example ex54 on the Curie architect
 \end{center}
 \end{table*}
 
+\begin{figure}[htbp]
+\centering
+  \includegraphics[width=0.45\textwidth]{nb_iter_sec_ex54_curie}
+\caption{Number of iterations per second with ex54 and the same parameters than in Table~\ref{tab:05}}
+\label{fig:02}
+\end{figure}
+
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