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A method of accelerating stationary iterative methods for solving linear systems

Published online by Cambridge University Press:  17 February 2009

G. K. Robinson
G. K. Robinson
Affiliation:
CSIRO Division of Mathematics and Statistics, Private Bag 10, Clayton, Vic. 3168, Australia.
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Abstract

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The speed of convergence of stationary iterative techniques for solving simultaneous linear equations may be increased by using a method similar to conjugate gradients but which does not require the stationary iterative technique to be symmetrisable. The method of refinement is to find linear combinations of iterates from a stationary technique which minimise a quadratic form. This basic method may be used in several ways to construct refined versions of the simple technique. In particular, quadratic forms of much less than full rank may be used. It is suggested that the method is likely to be competitive with other techniques when the number of linear equations is very large and little is known about the properties of the system of equations. A refined version of the Gauss-Seidel technique was found to converge satisfactorily for two large systems of equations arising in the estimation of genetic merit of dairy cattle.

Type
Research Article
Information
The ANZIAM Journal , Volume 30 , Issue 1 , July 1988 , pp. 1 - 23
Copyright
Copyright © Australian Mathematical Society 1988

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