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 , where the matrix *A* is irreducible and diagonally dominant, we obtain bounds for the spectral radius of the 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 of the SOR method, and we improve the results of Theorems 5, 6 of [3] for the AOR method.

**[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