Convergence of the accelerated overrelaxation method

Dragoslav Herceg; Ljiljana Cvetković

Aplikace matematiky (1989)

  • Volume: 34, Issue: 6, page 475-479
  • ISSN: 0862-7940

Abstract

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The convergence of the Accelerated Overrelaxation (AOR) method is discussed. It is shown that the intervals of convergence for the parameters σ and ω are not always of the following form: 0 ω ω 1 , - σ 1 σ σ 2 , σ 1 , σ 2 0 .

How to cite

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Herceg, Dragoslav, and Cvetković, Ljiljana. "Convergence of the accelerated overrelaxation method." Aplikace matematiky 34.6 (1989): 475-479. <http://eudml.org/doc/15603>.

@article{Herceg1989,
abstract = {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: $0\le \omega \le \omega _1, -\sigma _1\le \sigma \le \sigma _2, \sigma _1, \sigma _2\ge 0$.},
author = {Herceg, Dragoslav, Cvetković, Ljiljana},
journal = {Aplikace matematiky},
keywords = {accelerated overrelaxation method; AOR method; successive overrelaxation; rate of convergence; relaxation parameter; interval of convergence; iterative process; accelerated overrelaxation method; AOR method; successive overrelaxation; rate of convergence; relaxation parameter; interval of convergence},
language = {eng},
number = {6},
pages = {475-479},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Convergence of the accelerated overrelaxation method},
url = {http://eudml.org/doc/15603},
volume = {34},
year = {1989},
}

TY - JOUR
AU - Herceg, Dragoslav
AU - Cvetković, Ljiljana
TI - Convergence of the accelerated overrelaxation method
JO - Aplikace matematiky
PY - 1989
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 34
IS - 6
SP - 475
EP - 479
AB - 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: $0\le \omega \le \omega _1, -\sigma _1\le \sigma \le \sigma _2, \sigma _1, \sigma _2\ge 0$.
LA - eng
KW - accelerated overrelaxation method; AOR method; successive overrelaxation; rate of convergence; relaxation parameter; interval of convergence; iterative process; accelerated overrelaxation method; AOR method; successive overrelaxation; rate of convergence; relaxation parameter; interval of convergence
UR - http://eudml.org/doc/15603
ER -

References

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  1. G. Avdelas A. Hadjidimos, Some theoretical and computational results concerning the accelerated overrelaxation (AOR) method, Anal. Numer. Theor. Approx. 9 (1980), 5-10. (1980) Zbl0445.65018MR0617249
  2. Lj. Cvetkovič D. Herceg, 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) Zbl0704.65017MR0805793
  3. Lj. Cvetkovič D. Herceg, Convergence theory for AOR method, Journal of Computational Mathematics (in print). Zbl0704.65017
  4. Lj. Cvetkovič D. Herceg, An improvement for the area of convergence of the AOR method, Anal. Numer. Theor. Approx. 16 (1987), 109-115. (1987) Zbl0641.65027MR0986095
  5. A. Hadjidimos, Accelerated overrelaxation method, Math. Соmр. 32 (1978), 149-157. (1978) Zbl0382.65015MR0483340
  6. S. Hague, 10.1093/imanum/7.3.307, IMA J. Numer. Anal. 7 (1987), 307-311. (1987) MR0968526DOI10.1093/imanum/7.3.307
  7. M. Martins, An improvement for the area of convergence of the accelerated overrelaxation iterative method, Anal. Numer. Theor. Approx. 12 (1983), 65 - 76. (1983) Zbl0527.65023MR0743917

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