Note on irreducible diagonally dominant matrices and the convergence of the AOR iterative method
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- by M. Madalena Martins PDF
- Math. Comp. 37 (1981), 101-103 Request permission
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
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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.
- Apostolos Hadjidimos, Accelerated overrelaxation method, Math. Comp. 32 (1978), no. 141, 149–157. MR 483340, DOI 10.1090/S0025-5718-1978-0483340-6
- M. Madalena Martins, On an accelerated overrelaxation iterative method for linear systems with strictly diagonally dominant matrix, Math. Comp. 35 (1980), no. 152, 1269–1273. MR 583503, DOI 10.1090/S0025-5718-1980-0583503-4
- Richard S. Varga, Matrix iterative analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1962. MR 0158502
- David M. Young, Iterative solution of large linear systems, Academic Press, New York-London, 1971. MR 0305568
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Math. Comp. 37 (1981), 101-103
- MSC: Primary 65F10
- DOI: https://doi.org/10.1090/S0025-5718-1981-0616363-4
- MathSciNet review: 616363