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The sigma-SOR algorithm and the optimal strategy for the utilization of the SOR iterative method


Author: Zbigniew I. Woźnicki
Journal: Math. Comp. 62 (1994), 619-644
MSC: Primary 65F10; Secondary 65B99
DOI: https://doi.org/10.1090/S0025-5718-1994-1212270-6
Corrigendum: Math. Comp. 66 (1997), 1769-1769.
MathSciNet review: 1212270
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Abstract | References | Similar Articles | Additional Information

Abstract: The paper describes, discusses, and numerically illustrates the method for obtaining a priori estimates of the optimum relaxation factor in the SOR iteration method. The computational strategy of this method uses the so-called Sigma-SOR algorithm based on the theoretical result proven in the paper. The method presented is especially efficient for problems with slowly convergent iteration process and in this case is strongly competitive with adaptive procedures used for determining dynamically the optimum relaxation factor during the course of the SOR solution.


References [Enhancements On Off] (What's this?)

  • [1] L. A. Hageman and D. Young, Applied iterative methods, Academic Press, New York, 1981. MR 630192 (83c:65064)
  • [2] B. A. Carré, The determination of the optimum accelerating factor for successive over-relaxation, Comput. J. 4 (1961), 73-78.
  • [3] H. E. Kulsrud, A practical technique for the determination of the optimum relaxation factor of the successive over-relaxation method, Comm. ACM 4 (1961), 184-187. MR 0143336 (26:895)
  • [4] L. A. Hageman and R. B. Kellogg, Estimating optimum relaxation factors for use in the successive over relaxation and the Chebyshev polynomial methods of iteration, WAPD-TM-592, 1966.
  • [5] J. H. Wilkinson, The algebraic eigenvalue problem, Oxford Univ. Press, London, 1965. MR 0184422 (32:1894)
  • [6] L. A. Hageman and R. S. Varga, Block iterative methods for cyclically reduced matrix equations, Numer. Math. 6 (1964), 106-119. MR 0166912 (29:4185)
  • [7] P. Concus, G. H. Golub, and G. Meurant, Block preconditioning for the conjugate gradient method, SIAM J. Sci. Statist. Comput. 6 (1985), 220-252. MR 773293 (87c:65035a)
  • [8] Z. I. Woźnicki, On numerical analysis of conjugate gradient method, Japan J. Indust. Appl. Math. 10 (1993), 487-519. MR 1247879 (95e:65034)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1994-1212270-6
Keywords: SOR iteration method, power method, acceleration of convergence, eigenvalues of iteration matrix, estimation of optimum relaxation factor
Article copyright: © Copyright 1994 American Mathematical Society

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