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5th IMACS Conference on Iterative Methods in Scientific Computing
May 28-31, 2001
Foundation for Research and Technology - Hellas (FORTH)
Heraklion, Crete, Greece

Organizers
Apostolos Hadjidimos, Elias Houstis, Emmanuel Vavalis

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Optimal Complex Semi-iterative Methods Applied to SOR in the Case of Intersecting Lines Spectra
by
N.S. Stylianopoulos
Department of Mathematics and Statistics, University of Cyprus, P.O. Box 20537, CY-1678 Nicosia, Cyprus
Coauthors: A. Hadjimidos (Mathematics Department, University of Crete, GREECE)

We consider the application of semi-iterative methods to the standard successive over-relaxation method (SOR), with complex parameter \omega, under the assumptions that the associated Jacobi matrix J is consistently ordered and weakly cyclic of index 2 and that the spectrum \sigma(J) belongs to (a) the line segment [-\mu1, \mu1], \mu1 in \scriptscriptstyle | C\{1}; (b) the intersecting lines [-\mu1, \mu1] \cup [-\mu2, \mu2], \mu1, \mu2 in \scriptscriptstyle | C\{1}. By using results from potential theory in the complex domain, we analyse completely the case (a) and provide the region of optimal choice of \omega in \scriptscriptstyle | C, along with the exact region of convergence, for the case (b). Our work was motivated by recent results of M. Eiermann and R.S. Varga (Linear Algebra Appl., 182, pp. 257-277 (1993), and pp. 47-73 in Numerical Linear Algebra, L. Reichel (ed.) et al, de Gruyter, 1993).

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Date received: March 14, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts. Document # cagm-25.