From: Christophe Guyeux <guyeux@gmail.com>
Date: Fri, 10 Oct 2014 11:31:18 +0000 (+0200)
Subject: Début de la preuve de convergence.
X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/GMRES2stage.git/commitdiff_plain/95fea275e81cda394a2278d66259fce8f4df5e8c?ds=inline

Début de la preuve de convergence.
---

diff --git a/paper.tex b/paper.tex
index e512018..e927821 100644
--- a/paper.tex
+++ b/paper.tex
@@ -752,6 +752,11 @@ If $A$ is a positive real matrix, then the TSIRM algorithm is convergent.
 \end{proposition}
 
 \begin{proof}
+Let $r_k = b-Ax_k$, where $x_k$ is the approximation of the solution after the
+$k$-th iterate of TSIRM.
+We will prove that $r_k \rightarrow 0$ when $k \rightarrow +\infty$.
+
+
 \end{proof}
 
 %%%*********************************************************
@@ -1055,4 +1060,3 @@ Curie and Juqueen respectively based in France and Germany.
 
 % that's all folks
 \end{document}
-