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On the convergence of the generalized AOR method. (English) Zbl 0872.65028

The overrelaxation method with individual overrelaxation factors for the rows is called the accelerated overrelaxation (AOR) method. Special cases as positive definite matrices, and \(H\)-, \(L\)-, or \(M\)-matrices are considered.
Reviewer: D.Braess (Bochum)

MSC:

65F10 Iterative numerical methods for linear systems
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References:

[1] Berman, A.; Plemmons, R. J., Nonnegative Matrices in the Mathematical Sciences (1979), Academic: Academic New York · Zbl 0484.15016
[2] Evans, D. J.; Martins, M. M., On the convergence of the extrapolated AOR method, Internat. J. Computer Math., 43, 161-171 (1992) · Zbl 0754.65032
[3] Hadjidimos, A., Accelerated overrelaxation method, Math. Comp., 32, 149-157 (1978) · Zbl 0382.65015
[4] James, K. R., Convergence of matrix iterations subject to diagonal dominance, SIAM J. Numer. Anal., 12, 478-484 (1973) · Zbl 0255.65019
[5] Ortega, J. M.; Plemmons, R. J., Extension of the Ostrowski-Reich theorem for SOR iterations, Linear Algebra Appl., 28, 177-191 (1979) · Zbl 0416.65024
[6] Rheinholdt, W. C.; Vandergraft, J. S., A simple approach to the Perron-Frobenius theory for positive operators on general partially-ordered finite-dimensional linear spaces, Math. Comp., 27, 139-145 (1973) · Zbl 0255.15017
[7] Song, Y., Konvergenzkriterien für das verallgemeinerte AOR-Verfahren, Z. Angew. Math. Mech., 72, 445-447 (1992) · Zbl 0767.65023
[8] Varga, R. S., Matrix Iterative Analysis (1962), Prentice-Hall: Prentice-Hall Englewood Cliffs, N.J · Zbl 0133.08602
[9] Varga, R. S., On recurring theorems on diagonal dominance, Linear Algebra Appl., 13, 1-9 (1976) · Zbl 0336.15007
[10] Wilkinson, J. H., The Algebraic Eigenvalue Problem (1965), Oxford U.P: Oxford U.P New York · Zbl 0258.65037
[11] Young, D. M., Iterative Solution of Large Linear Systems (1971), Academic: Academic New York · Zbl 0204.48102
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