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A Convergence Analysis of the MINRES Method for Some Hermitian Indefinite Systems

Part of: Numerical linear algebra Numerical analysis: Ordinary differential equations Partial differential equations, boundary value problems

Published online by Cambridge University Press:  31 January 2018

Ze-Jia Xie ,
Xiao-Qing Jin  and
Zhi Zhao
Ze-Jia Xie*
Affiliation:
Department of Mathematics and Data Science, Dongguan University of Technology, Dongguan, 523808, China
Xiao-Qing Jin*
Affiliation:
Department of Mathematics, University of Macau, Macao
Zhi Zhao*
Affiliation:
Department of Mathematics, School of Sciences, Hangzhou Dianzi University, Hangzhou, 310018, China
*
*Corresponding author. Email addresses:xiezejia2012@gmail.com (Z.-J. Xie), xqjin@umac.mo (X.-Q. Jin), zhaozhi231@163.com (Z. Zhao)
*Corresponding author. Email addresses:xiezejia2012@gmail.com (Z.-J. Xie), xqjin@umac.mo (X.-Q. Jin), zhaozhi231@163.com (Z. Zhao)
*Corresponding author. Email addresses:xiezejia2012@gmail.com (Z.-J. Xie), xqjin@umac.mo (X.-Q. Jin), zhaozhi231@163.com (Z. Zhao)
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Abstract

Some convergence bounds of the minimal residual (MINRES) method are studied when the method is applied for solving Hermitian indefinite linear systems. The matrices of these linear systems are supposed to have some properties so that their spectra are all clustered around ±1. New convergence bounds depending on the spectrum of the coefficient matrix are presented. Some numerical experiments are shown to demonstrate our theoretical results.

Keywords

MINRESConvergence boundHermitian indefiniteToeplitz system

MSC classification

Secondary: 65F10: Iterative methods for linear systems 65F15: Eigenvalues, eigenvectors 65L05: Initial value problems 65N22: Solution of discretized equations
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 7 , Issue 4 , November 2017 , pp. 827 - 836
Copyright
Copyright © Global-Science Press 2017 

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