On the convergence of generalized parallel multisplittingiterative methods for semidefinite linear systems

Yanxing Cui; Chuanlong Wang; Ruiping  Wen

doi:10.3934/naco.2012.2.863

Article Contents

2012, Volume 2, Issue 4: 863-873. Doi: 10.3934/naco.2012.2.863

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On the convergence of generalized parallel multisplitting iterative methods for semidefinite linear systems

1.
Department of Mathematics, Changzhi University, Changzhi 046011, Shanxi Province
2.
Department of Mathematics, Taiyuan Normal University, Taiyuan 030012, Shanxi Province

Received: January 2012

Revised: October 2012

Published: November 2012

Abstract / Introduction Related Papers Cited by

Abstract

In this paper, we present the generalized stationary and nonstationary multisplitting iterative methods for positive semidefinite linear systems. We study the convergence theories of new methods and show that the quotient convergence and convergence of stationary parallel multisplitting method are equivalent under a concise condition. Finally, we prove that the generalized nonstationary parallel multisplitting method is quotient convergence with general weighting matrices.

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Mathematics Subject Classification: 58F15, 58F17.

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