From: lilia <lilia@agora>
Date: Fri, 10 Oct 2014 11:59:15 +0000 (+0200)
Subject: mMerge branch 'master' of ssh://bilbo.iut-bm.univ-fcomte.fr/GMRES2stage
X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/GMRES2stage.git/commitdiff_plain/8aeef74d04b37c2601749676e053a538ba3785cd?hp=acead508c1f820b919aa203c78668e5e645cc9b8

mMerge branch 'master' of ssh://bilbo.iut-bm.univ-fcomte.fr/GMRES2stage

Conflicts:
	paper.tex
---

diff --git a/paper.tex b/paper.tex
index bf9e767..f1becbd 100644
--- a/paper.tex
+++ b/paper.tex
@@ -745,7 +745,22 @@ where $\alpha = \lambda_min(M)^2$ and $\beta = \lambda_max(A^T A)$, which proves
 the convergence of GMRES($m$) for all $m$ under that assumption regarding $A$.
 \end{proposition}
 
+<<<<<<< HEAD
 
+=======
+We can now claim that,
+\begin{proposition}
+If $A$ is a positive real matrix and GMRES($m$) is used as solver, 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 $k \rightarrow +\infty$.
+
+Each step of the TSIRM algorithm 
+\end{proof}
+>>>>>>> 84e15020344b77e5497c4a516cc20b472b2914cd
 
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