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Note on irreducible diagonally dominant matrices and the convergence of the AOR iterative method


Author: M. Madalena Martins
Journal: Math. Comp. 37 (1981), 101-103
MSC: Primary 65F10
DOI: https://doi.org/10.1090/S0025-5718-1981-0616363-4
MathSciNet review: 616363
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Abstract: Considering the linear systems $ Ax = b$, where the matrix A is irreducible and diagonally dominant, we obtain bounds for the spectral radius of the $ {L_{r,\omega }}$ matrix of the AOR method and we achieve the convergence conditions given in [2] by a different method.

If A is strictly diagonally dominant, we get larger intervals for the parameter $ \omega $ of the SOR method, and we improve the results of Theorems 5, 6 of [3] for the AOR method.


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

  • [1] G. Avdelas, A. Hadjidimos & A. Yeyios, Some Theoretical and Computational Results Concerning the Accelerated Overrelaxation (AOR) Method, Tech. Report No. 8, Department of Mathematics, University of Ioannina, Ioannina, Greece, 1978.
  • [2] A. Hadjidimos, "Accelerated overrelaxation method," Math. Comp., v. 32, 1978, pp. 149-157. MR 0483340 (58:3353)
  • [3] M. Martins, "On an accelerated overrelaxation iterative method for linear systems with strictly diagonally dominant matrix," Math. Comp., v. 35, 1980, pp. 1269-1273. MR 583503 (83h:65045)
  • [4] R. S. Varga, Matrix Iterative Analysis, Prentice-Hall, Englewood Cliffs, N. J., 1962. MR 0158502 (28:1725)
  • [5] D. M. Young, Iterative Solution of Large Linear Systems, Academic Press, New York, 1971. MR 0305568 (46:4698)

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DOI: https://doi.org/10.1090/S0025-5718-1981-0616363-4
Article copyright: © Copyright 1981 American Mathematical Society

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