International Journal of Computer Mathematics, ( ISI ), Volume (2016), No (1), Year (2016-1) , Pages (1-17)

Title : ( An iterative method for solving the continuous sylvester equation by emphasizing on the skewhermitian parts of the coefficient matrices )

Authors: Mohammad Khorsand Zak , Faezeh Toutounian Mashhad ,

Citation: BibTeX | EndNote

We present an iterative method based on the Hermitian and skew-Hermitian splitting (HSS) for solving the continuous Sylvester equation. By using the HSS of the coefficient matrices A and B, we establish a method which is practically inner/outer iterations, by employing a conjugate gradient on the normal equations (CGNR)-like method as inner iteration to approximate each outer iterate, while each outer iteration is induced by a convergent splitting of the coefficient matrices. Via this method, a Sylvester equation with coefficient matrices SA and SB (which are the skew-Hermitian part of A and B, respectively) is solved iteratively by a CGNR-like method. Convergence conditions of this method are studied and numerical examples 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

, CGNR; Sylvester equation; Hermitian and skew, Hermitian splitting; preconditioning; nested
برای دانلود از شناسه و رمز عبور پرتال پویا استفاده کنید.

@article{paperid:1054814,
author = {Mohammad Khorsand Zak and Toutounian Mashhad, Faezeh},
title = {An iterative method for solving the continuous sylvester equation by emphasizing on the skewhermitian parts of the coefficient matrices},
journal = {International Journal of Computer Mathematics},
year = {2016},
volume = {2016},
number = {1},
month = {January},
issn = {0020-7160},
pages = {1--17},
numpages = {16},
keywords = {CGNR; Sylvester equation; Hermitian and skew-Hermitian splitting; preconditioning; nested iterations},
}

[Download]

%0 Journal Article
%T An iterative method for solving the continuous sylvester equation by emphasizing on the skewhermitian parts of the coefficient matrices
%A Mohammad Khorsand Zak
%A Toutounian Mashhad, Faezeh
%J International Journal of Computer Mathematics
%@ 0020-7160
%D 2016

[Download]