From: lilia <lilia@amazigh.bordeaux.inria.fr>
Date: Mon, 18 Aug 2014 15:08:09 +0000 (+0200)
Subject: v2
X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/GMRES2stage.git/commitdiff_plain/1082caa290770800e8a7f6815ed153931cd93460?ds=sidebyside

v2
---

diff --git a/paper.tex b/paper.tex
index 381954b..185bbf3 100644
--- a/paper.tex
+++ b/paper.tex
@@ -553,24 +553,25 @@ Iterative Krylov methods; sparse linear systems; error minimization; PETSC; %à
 %%%*********************************************************
 %%%*********************************************************
 \section{A Krylov two-stage algorithm}
+We propose a two-stage algorithm to solve large sparse linear systems of the form $Ax=b$ based on iterative Krylov sub-space methods.
 
 
 \begin{algorithm}[!h]
 \caption{A Krylov two-stage algorithm}
 \begin{algorithmic}[1]
-\Input $A$ (sparse matrix), $b$ (right-hand side)
-\Output $x$ (solution vector)\vspace{0.2cm}
-\State Set the initial guess $x^0$
-\For {$k=1,2,3,\ldots$ until convergence}
-\State Solve iteratively $Ax^k=b$
-\State Add vector $x^k$ to Krylov basis $S$
-\If {$k$ mod $s=0$ {\bf and} not convergence}
-\State Compute dense matrix $R=AS$
-\State Solve least-squares problem $\|b-R\alpha\|_2$
-\State Compute minimizer $x^k=S\alpha$
-\State Reinitialize Krylov basis $S$
-\EndIf
-\EndFor
+  \Input $A$ (sparse matrix), $b$ (right-hand side)
+  \Output $x$ (solution vector)\vspace{0.2cm}
+  \State Set the initial guess $x^0$
+  \For {$k=1,2,3,\ldots$ until convergence}
+    \State Solve iteratively $Ax^k=b$
+    \State Add vector $x^k$ to Krylov basis $S$
+    \If {$k$ mod $s=0$ {\bf and} not convergence}
+      \State Compute dense matrix $R=AS$
+      \State Solve least-squares problem $\|b-R\alpha\|_2$
+      \State Compute minimizer $x^k=S\alpha$
+      \State Reinitialize Krylov basis $S$
+    \EndIf
+  \EndFor
 \end{algorithmic}
 \label{algo:01}
 \end{algorithm}