# Convergence of the accelerated overrelaxation method

Dragoslav Herceg; Ljiljana Cvetković

Aplikace matematiky (1989)

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

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topHerceg, 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

top- G. Avdelas A. Hadjidimos, Some theoretical and computational results concerning the accelerated overrelaxation (AOR) method, Anal. Numer. Theor. Approx. 9 (1980), 5-10. (1980) MR0617249
- 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) MR0805793
- Lj. Cvetkovič D. Herceg, Convergence theory for AOR method, Journal of Computational Mathematics (in print).
- Lj. Cvetkovič D. Herceg, An improvement for the area of convergence of the AOR method, Anal. Numer. Theor. Approx. 16 (1987), 109-115. (1987) MR0986095
- A. Hadjidimos, Accelerated overrelaxation method, Math. Соmр. 32 (1978), 149-157. (1978) Zbl0382.65015MR0483340
- S. Hague, 10.1093/imanum/7.3.307, IMA J. Numer. Anal. 7 (1987), 307-311. (1987) MR0968526DOI10.1093/imanum/7.3.307
- 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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