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
%%%*********************************************************
%%%*********************************************************
