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Title of Journal: Numer Math

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Abbravation: Numerische Mathematik

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Springer-Verlag

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DOI

10.1007/bf00697159

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0945-3245

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On generalized successive overrelaxation methods f

Authors: ZhongZhi Bai Beresford N Parlett ZengQi Wang
Publish Date: 2005/09/29
Volume: 102, Issue: 1, Pages: 1-38
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Abstract

For the augmented system of linear equations Golub Wu and Yuan recently studied an SORlike method BIT 41200171–85 By further accelerating it with another parameter in this paper we present a generalized SOR GSOR method for the augmented linear system We prove its convergence under suitable restrictions on the iteration parameters and determine its optimal iteration parameters and the corresponding optimal convergence factor Theoretical analyses show that the GSOR method has faster asymptotic convergence rate than the SORlike method Also numerical results show that the GSOR method is more effective than the SORlike method when they are applied to solve the augmented linear system This GSOR method is further generalized to obtain a framework of the relaxed splitting iterative methods for solving both symmetric and nonsymmetric augmented linear systems by using the techniques of vector extrapolation matrix relaxation and inexact iteration Besides we also demonstrate a complete version about the convergence theory of the SORlike method

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