The convergence of the Accelerated Overrelaxation (AOR) method is discussed. It is shown that the intervals of convergence for the parameters $\sigma$ and $\omega$ are not always of the following form: $0\leq \omega \leq \omega_1, -\sigma_1\leq\sigma\leq\sigma_2, \sigma_1, \sigma_2\geq 0$.
@article{104378, author = {Dragoslav Herceg and Ljiljana Cvetkovi\'c}, title = {Convergence of the accelerated overrelaxation method}, journal = {Applications of Mathematics}, volume = {34}, year = {1989}, pages = {475-479}, zbl = {0697.65020}, mrnumber = {1026512}, language = {en}, url = {http://dml.mathdoc.fr/item/104378} }
Herceg, Dragoslav; Cvetković, Ljiljana. Convergence of the accelerated overrelaxation method. Applications of Mathematics, Tome 34 (1989) pp. 475-479. http://gdmltest.u-ga.fr/item/104378/
Some theoretical and computational results concerning the accelerated overrelaxation (AOR) method, Anal. Numer. Theor. Approx. 9 (1980), 5-10. (1980) | MR 0617249
Some sufficient conditions for convergence AOR-method, In: Numerical Methods and Approximation Theory, G. V. Milovanič, ed., Faculty of Electronic Engineering, Niš, 1984, 143-148. (1984) | MR 0805793
Convergence theory for AOR method, Journal of Computational Mathematics (in print).
An improvement for the area of convergence of the AOR method, Anal. Numer. Theor. Approx. 16 (1987), 109-115. (1987) | MR 0986095
Accelerated overrelaxation method, Math. Соmр. 32 (1978), 149-157. (1978) | MR 0483340 | Zbl 0382.65015
Convergence of the successive overrelaxation method, IMA J. Numer. Anal. 7 (1987), 307-311. (1987) | Article | MR 0968526
An improvement for the area of convergence of the accelerated overrelaxation iterative method, Anal. Numer. Theor. Approx. 12 (1983), 65 - 76. (1983) | MR 0743917 | Zbl 0527.65023