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On an accelerated overrelaxation iterative method for linear systems with strictly diagonally dominant matrix


Author: M. Madalena Martins
Journal: Math. Comp. 35 (1980), 1269-1273
MSC: Primary 65F10
DOI: https://doi.org/10.1090/S0025-5718-1980-0583503-4
MathSciNet review: 583503
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Abstract: We consider a linear system $ Ax = b$ of n simultaneous equations, where A is a strictly diagonally dominant matrix. We get bounds for the spectral radius of the matrix $ {L_{r,\omega }}$, which is accociated with the Accelerated Overrelaxation iterative method (AOR).

Sufficient conditions for the convergence of that method will be given, which improve the results of Theorem 3, Section 4 of [2], applied to this type of matrices.


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

  • [1] A. HADJIDIMOS, "Accelerated overrelaxation method," Math. Comp., v. 32, 1978, pp. 149-157. MR 0483340 (58:3353)
  • [2] A. HADJIDIMOS & A. YEYIOS, The Principle of Extrapolation in Connection with the Accelerated Overrelaxation (AOR) Method, T. R. No. 16, Department of Mathematics, University of Ioannina, Ioannina, Greece, 1978.
  • [3] G. AVDELAS, A. HADJIDIMOS & A. YEYIOS, Some Theoretical and Computational Results Concerning the Accelerated Overrelaxation (AOR) Method, T. R. No. 8, Department of Mathematics, University of Ioannina, Ioannina, Greece, 1978.
  • [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 and London, 1971. MR 0305568 (46:4698)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1980-0583503-4
Article copyright: © Copyright 1980 American Mathematical Society

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