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SOR-like Methods with Optimization Model for Augmented Linear Systems

Part of: Basic linear algebra Numerical linear algebra

Published online by Cambridge University Press:  31 January 2017

Rui-Ping Wen ,
Su-Dan Li  and
Guo-Yan Meng
Rui-Ping Wen*
Affiliation:
Department of Mathematics, Taiyuan Normal University, Taiyuan, 030012, China
Su-Dan Li*
Affiliation:
Department of Mathematics, Taiyuan Normal University, Taiyuan, 030012, China
Guo-Yan Meng*
Affiliation:
Department of Mathematics, Xinzhou Teachers College, Xinzhou, 034000, China
*
*Corresponding author. Email addresses:wenrp@163.com (R.-P. Wen), lisudan1990@163.com (S.-D. Li), mgy1226@126.com (G.-Y. Meng)
*Corresponding author. Email addresses:wenrp@163.com (R.-P. Wen), lisudan1990@163.com (S.-D. Li), mgy1226@126.com (G.-Y. Meng)
*Corresponding author. Email addresses:wenrp@163.com (R.-P. Wen), lisudan1990@163.com (S.-D. Li), mgy1226@126.com (G.-Y. Meng)
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Abstract

There has been a lot of study on the SOR-like methods for solving the augmented system of linear equations since the outstanding work of Golub, Wu and Yuan (BIT 41(2001)71-85) was presented fifteen years ago. Based on the SOR-like methods, we establish a class of accelerated SOR-like methods for large sparse augmented linear systems by making use of optimization technique, which will find the optimal relaxation parameter ω by optimization models. We demonstrate the convergence theory of the new methods under suitable restrictions. The numerical examples show these methods are effective.

Keywords

SOR-like methodoptimizationaugmented linear systemsconvergence

MSC classification

Secondary: 65F10: Iterative methods for linear systems 65F50: Sparse matrices 15A06: Linear equations
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 7 , Issue 1 , February 2017 , pp. 101 - 115
Copyright
Copyright © Global-Science Press 2017 

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