International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 2, Pages 361-370

The extrapolated successive overrelaxation (ESOR) method for consistently ordered matrices

N. M. Missirlis1 and D. J. Evans2

1Department of Applied Mathematics, University of Athens, Panepistimiopolis 621, Athens, Greece
2Department of Computer Studies, Loughborough University of Technology, Loughborough, Leicestershire, UK

Received 30 September 1982; Revised 2 April 1983

Copyright © 1984 N. M. Missirlis and D. J. Evans. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper develops the theory of the Extrapolated Successive Overrelaxation (ESOR) method as introduced by Sisler in [1], [2], [3] for the numerical solution of large sparse linear systems of the form Au=b, when A is a consistently ordered 2-cyclic matrix with non-vanishing diagonal elements and the Jacobi iteration matrix B possesses only real eigenvalues. The region of convergence for the ESOR method is described and the optimum values of the involved parameters are also determined. It is shown that if the minimum of the moduli of the eigenvalues of B, μ¯ does not vanish, then ESOR attains faster rate of convergence than SOR when 1μ¯2<(1μ¯2)12, where μ¯ denotes the spectral radius of B.