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Positive Definite and Semi-Definite Splitting Methods for Non-Hermitian Positive Definite Linear Systems

Positive Definite and Semi-Definite Splitting Methods for Non-Hermitian Positive Definite Linear Systems

Year:    2016

Author:    Na Huang, Changfeng Ma

Journal of Computational Mathematics, Vol. 34 (2016), Iss. 3 : pp. 300–316

Abstract

In this paper, we further generalize the technique for constructing the normal (or positive definite) and skew-Hermitian splitting iteration method for solving large sparse non-Hermitian positive definite system of linear equations. By introducing a new splitting, we establish a class of efficient iteration methods, called positive definite and semi-definite splitting (PPS) methods, and prove that the sequence produced by the PPS method converges unconditionally to the unique solution of the system. Moreover, we propose two kinds of typical practical choices of the PPS method and study the upper bound of the spectral radius of the iteration matrix. In addition, we show the optimal parameters such that the spectral radius achieves the minimum under certain conditions. Finally, some numerical examples are given to demonstrate the effectiveness of the considered methods.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1511-m2015-0299

Journal of Computational Mathematics, Vol. 34 (2016), Iss. 3 : pp. 300–316

Published online:    2016-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    17

Keywords:    Linear systems Splitting method Non-Hermitian matrix Positive definite matrix Positive semi-definite matrix Convergence analysis.

Author Details

Na Huang Email

Changfeng Ma Email

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