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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.


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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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