Début de la preuve de convergence.

[GMRES2stage.git] / paper.tex

diff --git a/paper.tex b/paper.tex
index e512018b8fd2b0bf94de9dbf5cdd4b83a8264a8f..e927821335a5e68dbe42b6331e012524088dcebb 100644 (file)
--- 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}
 \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}
 
 %%%*********************************************************
 \end{proof}
 
 %%%*********************************************************


@@ -1055,4 +1060,3 @@ Curie and Juqueen respectively based in France and Germany.
 
 % that's all folks
 \end{document}
 
 % that's all folks
 \end{document}

-