On the convergence of splittings for semidefinite linear systems

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Detail(s)

Original languageEnglish
Pages (from-to)2555-2566
Journal / PublicationLinear Algebra and Its Applications
Volume429
Issue number10
Publication statusPublished - 1 Nov 2008

Abstract

Recently, Lee et al. [Young-ju Lee, Jinbiao Wu, Jinchao Xu, Ludmil Zikatanov, On the convergence of iterative methods for semidefinite linear systems, SIAM J. Matrix Anal. Appl. 28 (2006) 634-641] introduce new criteria for the semi-convergence of general iterative methods for semidefinite linear systems based on matrix splitting. The new conditions generalize the classical notion of P-regularity introduced by Keller [H.B. Keller, On the solution of singular and semidefinite linear systems by iterations, SIAM J. Numer. Anal. 2 (1965) 281-290]. In view of their results, we consider here stipulations on a splitting A = M - N, which lead to fixed point systems such that, the iterative scheme converges to a weighted Moore-Penrose solution to the system Ax = b. Our results extend the result of Lee et al. to a more general case and we also show that it requires less restrictions on the splittings than Keller's P-regularity condition to ensure the convergence of iterative scheme. © 2008 Elsevier Inc. All rights reserved.

Research Area(s)

  • Hermitian positive semidefinite matrix, Iterative method, Linear system, Rectangular system, Regularity

Citation Format(s)

On the convergence of splittings for semidefinite linear systems. / Lin, Lijing; Wei, Yimin; Woo, Ching-Wah; Zhou, Jieyong.

In: Linear Algebra and Its Applications, Vol. 429, No. 10, 01.11.2008, p. 2555-2566.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review