Optimal successive overrelaxation iterative methods for P-cyclic matrices |
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Authors: | Michael Eiermann Wilhelm Niethammer Arden Ruttan |
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Institution: | (1) Institut für Praktische Mathematik, Universität Karlsruhe, D-7500 Karlsruhe, Federal Republic of Germany |
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Abstract: | Summary We consider linear systems whose associated block Jacobi matricesJ
p are weakly cyclic of indexp. In a recent paper, Pierce, Hadjidimos and Plemmons 13] proved that the block two-cyclic successive overrelaxation (SOR) iterative method is numerically more effective than the blockq-cyclic SOR-method, 2<qp, if the eigenvalues ofJ
p
p
are either all non-negative or all non-positive. Based on the theory of stationaryp-step methods, we give an alternative proof of their theorem. We further determine the optimal relaxation parameter of thep-cyclic SOR method under the assumption that the eigenvalues ofJ
p
p
are contained in a real interval, thereby extending results due to Young 19] (for the casep=2) and Varga 15] (forp>2). Finally, as a counterpart to the result of Pierce, Hadjidimos and Plemmons, we show that, under this more general assumption, the two-cyclic SOR method is not always superior to theq-cyclic SOR method, 2<qp.Dedicated to R. S. Varga on the occasion of his 60th birthdayResearch supported in part by the Deutsche Forschungsgemeinschaft |
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Keywords: | AMS(MOS): 65F10 CR: G1 3 |
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