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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