Petites modifs

diff --git a/paper.tex b/paper.tex
index e927821335a5e68dbe42b6331e012524088dcebb..02906282b5940c6d392f600c9b2942b2c86230b0 100644 (file)
--- a/paper.tex
+++ b/paper.tex
@@ -748,7 +748,7 @@ the convergence of GMRES($m$) for all $m$ under that assumption regarding $A$.
 
 We can now claim that,
 \begin{proposition}
 
 We can now claim that,
 \begin{proposition}

-If $A$ is a positive real matrix, then the TSIRM algorithm is convergent.
+If $A$ is a positive real matrix and GMRES($m$) is used as solver, then the TSIRM algorithm is convergent.

 \end{proposition}
 
 \begin{proof}
 \end{proposition}
 
 \begin{proof}


@@ -756,7 +756,7 @@ 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 $k \rightarrow +\infty$.
 
 $k$-th iterate of TSIRM.
 We will prove that $r_k \rightarrow 0$ when $k \rightarrow +\infty$.
 

-
+Each step of the TSIRM algorithm 

 \end{proof}
 
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 \end{proof}
 
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