\label{tab:01}
\end{center}
\end{table}
-Chosen parameters are detailed below. As by default the restart of GMRES is
-performed every 30 iterations, we have chosen to stop the GMRES every 30
-iterations (\emph{i.e.} $max\_iter_{kryl}=30$). $s$ is set to 8. CGLS is chosen
-to minimize the least-squares problem with the following parameters:
+Chosen parameters are detailed below.
+We have stopped the GMRES every 30
+iterations (\emph{i.e.}, $max\_iter_{kryl}=30$), which is the default
+setting of GMRES. $s$, for its part, has been set to 8. CGLS
+ minimizes the least-squares problem with parameters
$\epsilon_{ls}=1e-40$ and $max\_iter_{ls}=20$. The external precision is set to
-$\epsilon_{tsirm}=1e-10$. Those experiments have been performed on a Intel(R)
-Core(TM) i7-3630QM CPU @ 2.40GHz with the version 3.5.1 of PETSc.
+$\epsilon_{tsirm}=1e-10$. These experiments have been performed on an Intel(R)
+Core(TM) i7-3630QM CPU @ 2.40GHz with the 3.5.1 version of PETSc.
In Table~\ref{tab:02}, some experiments comparing the solving of the linear
For future work, the authors' intention is to investigate other kinds of
-matrices, problems, and inner solvers. The influence of all parameters must be
+matrices, problems, and inner solvers. In particular, the possibility
+to obtain a convergence of TSIRM in situations where the GMRES is divergent will be
+investigated. The influence of all parameters must be
tested too, while other methods to minimize the residuals must be regarded. The
number of outer iterations to minimize should become adaptative to improve the
overall performances of the proposal. Finally, this solver will be implemented
-inside PETSc. This would be very interesting because it would allow us to test
+inside PETSc, which would be of interest as it would allow us to test
all the non-linear examples and compare our algorithm with the other algorithm
implemented in PETSc.
