From 95fea275e81cda394a2278d66259fce8f4df5e8c Mon Sep 17 00:00:00 2001
From: Christophe Guyeux <guyeux@gmail.com>
Date: Fri, 10 Oct 2014 13:31:18 +0200
Subject: [PATCH 1/1] =?utf8?q?D=C3=A9but=20de=20la=20preuve=20de=20converg?=
 =?utf8?q?ence.?=
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---
 paper.tex | 6 +++++-
 1 file changed, 5 insertions(+), 1 deletion(-)

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}
-
-- 
2.39.5