From: Christophe Guyeux Date: Mon, 13 Oct 2014 12:21:07 +0000 (+0200) Subject: relecture X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/GMRES2stage.git/commitdiff_plain/23054d081ea510f87cf5c9d8ed9351034ffa8f45 relecture --- diff --git a/paper.tex b/paper.tex index c8e503d..c183ea4 100644 --- a/paper.tex +++ b/paper.tex @@ -601,15 +601,15 @@ is summarized while intended perspectives are provided. %%%********************************************************* \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 minimizes the residual over the current Krylov subspace until convergence in at