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\section{Related works}
\label{sec:02}
-Krylov subspace iteration methods have increasingly become useful and successful
-techniques for solving linear, nonlinear systems and eigenvalue problems,
-especially since the increase development of the
+Krylov subspace iteration methods have increasingly become key
+techniques for solving linear and nonlinear systems, or eigenvalue problems,
+especially since the increasing development of
preconditioners~\cite{Saad2003,Meijerink77}. One reason of the popularity of
-these methods is their generality, simplicity and efficiency to solve systems of
+these methods is their generality, simplicity, and efficiency to solve systems of
equations arising from very large and complex problems.
GMRES is one of the most widely used Krylov iterative method for solving sparse
-and large linear systems. It is developed by Saad and al.~\cite{Saad86} as a
+and large linear systems. It has been developed by Saad \emph{et al.}~\cite{Saad86} as a
generalized method to deal with unsymmetric and non-Hermitian problems, and
-indefinite symmetric problems too. In its original version called full GMRES, it
+indefinite symmetric problems too. In its original version called full GMRES, this algorithm
minimizes the residual over the current Krylov subspace until convergence in at
-most $n$ iterations, where $n$ is the size of the sparse matrix. It should be
-noticed that full GMRES is too expensive in the case of large matrices since the
+most $n$ iterations, where $n$ is the size of the sparse matrix.
+Full GMRES is however too much expensive in the case of large matrices, since the
required orthogonalization process per iteration grows quadratically with the
-number of iterations. For that reason, in practice GMRES is restarted after each
+number of iterations. For that reason, GMRES is restarted in practice after each
$m\ll n$ iterations to avoid the storage of a large orthonormal basis. However,
the convergence behavior of the restarted GMRES, called GMRES($m$), in many
cases depends quite critically on the value of $m$~\cite{Huang89}. Therefore in
