On the equivalence of SOR, SSOR and USSOR as applied to 1-ordered systems of linear equations
Open Access
- 1 January 1964
- journal article
- Published by Oxford University Press (OUP) in The Computer Journal
- Vol. 7 (1) , 72-75
- https://doi.org/10.1093/comjnl/7.1.72
Abstract
The method of symmetric successive over-relaxation (SSOR) was proposed by Sheldon (1955). It has been analyzed by Habetler and Wachspress (1961) and extended to the method of unsymmetric successive over-relaxation (USSOR) by D'Sylva and Miles (1964). The latter showed that for suitable choice of relaxation parameters asymptotic rates of convergence precisely half of those of the familiar method of successive over-relaxation (SOR) may be obtained when the method is applied to σ1-ordered systems of linear equations possessing Property A. The present paper shows that this factor is in fact spurious, and that, under the latter hypotheses, the methods of SOR, SSOR and USSOR are identical when applied to σ1-ordered systems of equations. it is hence shown that Chebyshev accelerated SSR (SSOR with unity relaxation parameter) becomes, in this case, identical with the Chebyshev accelerated Gauss-Seidel method (Varga (1957)). The theoretical results of D'Sylva and Miles and of this paper and the vastly different behaviours of the σ1- and σ2-orderings are emphasized by means of numerical examples.Keywords
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