From: lilia Date: Sun, 12 Oct 2014 08:05:26 +0000 (+0200) Subject: 12-10-2014 01 X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/GMRES2stage.git/commitdiff_plain/e724ad6659430fc142e69fbf048d62c5b945db67?hp=9fe58147d9a4e7a4182385b4a397fe96695b7862 12-10-2014 01 --- diff --git a/paper.tex b/paper.tex index 32e9a3f..118a2fb 100644 --- a/paper.tex +++ b/paper.tex @@ -601,6 +601,9 @@ is summarized while intended perspectives are provided. %%%********************************************************* \section{Related works} \label{sec:02} +Krylov subspace iteration methods have increasingly become very useful and popular for solving linear equations. + + %GMRES method is one of the most widely used iterative solvers chosen to deal with the sparsity and the large order of linear systems. It was initially developed by Saad \& al.~\cite{Saad86} to deal with non-symmetric and non-Hermitian problems, and indefinite symmetric problems too. The convergence of the restarted GMRES with preconditioning is faster and more stable than those of some other iterative solvers. %The next two chapters explore a few methods which are considered currently to be among the most important iterative techniques available for solving large linear systems. These techniques are based on projection processes, both orthogonal and oblique, onto Krylov subspaces, which are subspaces spanned by vectors of the form p(A)v where p is a polynomial. In short, these techniques approximate A −1 b by p(A)b, where p is a “good” polynomial. This chapter covers methods derived from, or related to, the Arnoldi orthogonalization. The next chapter covers methods based on Lanczos biorthogonalization.