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On the convergence of general stationary iterative methods for range-Hermitian singular linear systems

✍ Scribed by Naimin Zhang; Yi-Min Wei

Publisher: John Wiley and Sons
Year: 2010
Tongue: English
Weight: 142 KB
Volume: 17
Category: Article
ISSN: 1070-5325
DOI: 10.1002/nla.663

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✦ Synopsis

Abstract

General stationary iterative methods with a singular matrix M for solving range‐Hermitian singular linear systems are presented, some convergence conditions and the representation of the solution are also given. It can be verified that the general Ortega–Plemmons theorem and Keller theorem for the singular matrix M still hold. Furthermore, the singular matrix M can act as a good preconditioner for solving range‐Hermitian linear systems. Numerical results have demonstrated the effectiveness of the general stationary iterations and the singular preconditioner M. Copyright © 2009 John Wiley & Sons, Ltd.

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