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Preconditioned Positive-Definite and Skew-Hermitian Splitting Iteration Methods for Continuous Sylvester Equations AX + XB = C

Part of: Numerical linear algebra

Published online by Cambridge University Press:  31 January 2017

Rong Zhou ,
Xiang Wang  and
Xiao-Bin Tang
Rong Zhou
Affiliation:
Department of Mathematics, School of Sciences, Nanchang University, Nanchang 330031, China
Xiang Wang*
Affiliation:
Department of Mathematics, School of Sciences, Nanchang University, Nanchang 330031, China Numerical Simulation and High-Performance Computing Laboratory, School of Sciences, Nanchang University, Nanchang 330031, China
Xiao-Bin Tang
Affiliation:
School of Statistics, University of International Business and Economics, Beijing 100029, China
*
*Corresponding author. Email address:wangxiang49@ncu.edu.cn (X. Wang)
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Abstract

In this paper, we present a preconditioned positive-definite and skew-Hermitian splitting (PPSS) iteration method for continuous Sylvester equations AX + XB = C with positive definite/semi-definite matrices. The analysis shows that the PPSS iteration method will converge under certain assumptions. An inexact variant of the PPSS iteration method (IPPSS) has been presented and the analysis of its convergence property in detail has been discussed. Numerical results show that this new method is more efficient and robust than the existing ones.

Keywords

PPSS iteration methodIPPSS iteration methodSylvester equationsconvergence

MSC classification

Secondary: 65F10: Iterative methods for linear systems 65F50: Sparse matrices
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 7 , Issue 1 , February 2017 , pp. 55 - 69
Copyright
Copyright © Global-Science Press 2017 

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