Advances in Computational Mathematics, ( ISI ), Volume (40), No (113), Year (2013-9) , Pages (1-16)

Title : ( Nested splitting CG-like iterative method for solving the continuous Sylvester equation and preconditioning )

Authors: Mohammad Khorsand , Faezeh Toutounian Mashhad ,

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Abstract We present a nested splitting conjugate gradient iteration method for solving large sparse continuous Sylvester equation, in which both coefficient matrices are (non-Hermitian) positive semi-definite, and at least one of them is positive definite. This method is actually inner/outer iterations, which employs the Sylvester conjugate gradient method as inner iteration to approximate each outer iterate, while each outer iteration is induced by a convergent and Hermitian positive definite splitting of the coefficient matrices. Convergence conditions of this method are studied and numerical experiments show the efficiency of this method. In addition, we show that the quasi-Hermitian splitting can induce accurate, robust and effective preconditioned Krylov subspace methods

Keywords

Keywords Sylvester equation · Preconditioning · Conjugate gradient ·
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@article{paperid:1040042,
author = {Khorsand, Mohammad and Toutounian Mashhad, Faezeh},
title = {Nested splitting CG-like iterative method for solving the continuous Sylvester equation and preconditioning},
journal = {Advances in Computational Mathematics},
year = {2013},
volume = {40},
number = {113},
month = {September},
issn = {1019-7168},
pages = {1--16},
numpages = {15},
keywords = {Keywords Sylvester equation · Preconditioning · Conjugate gradient · Nested iterations},
}

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%0 Journal Article
%T Nested splitting CG-like iterative method for solving the continuous Sylvester equation and preconditioning
%A Khorsand, Mohammad
%A Toutounian Mashhad, Faezeh
%J Advances in Computational Mathematics
%@ 1019-7168
%D 2013

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