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On the convergence of general stationary iterative methods for range‐Hermitian singular linear systems
Author(s) -
Zhang Naimin,
Wei YiMin
Publication year - 2010
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.663
Subject(s) - preconditioner , mathematics , hermitian matrix , convergence (economics) , singular solution , matrix (chemical analysis) , iterative method , range (aeronautics) , linear system , mathematical analysis , pure mathematics , mathematical optimization , materials science , economics , composite material , economic growth
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.