# Two step extrapolation and optimum choice of relaxation factor of the extrapolated S.O.R. method

Aplikace matematiky (1988)

• Volume: 33, Issue: 3, page 177-196
• ISSN: 0862-7940

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## Abstract

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Limits of the extrapolation coefficients are rational functions of several poles with the largest moduli of the resolvent operator $R\left(\lambda ,T\right)={\left(\lambda I-T\right)}^{-1}$ and therefore good estimates of these poles could be calculated from these coefficients. The calculation is very easy for the case of two coefficients and its practical effect in finite dimensional space is considerable. The results are used for acceleration of S.O.R. method.

## How to cite

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Zítko, Jan. "Two step extrapolation and optimum choice of relaxation factor of the extrapolated S.O.R. method." Aplikace matematiky 33.3 (1988): 177-196. <http://eudml.org/doc/15536>.

@article{Zítko1988,
abstract = {Limits of the extrapolation coefficients are rational functions of several poles with the largest moduli of the resolvent operator $R(\lambda , T)=(\lambda I -T)^\{-1\}$ and therefore good estimates of these poles could be calculated from these coefficients. The calculation is very easy for the case of two coefficients and its practical effect in finite dimensional space is considerable. The results are used for acceleration of S.O.R. method.},
author = {Zítko, Jan},
journal = {Aplikace matematiky},
keywords = {two step extrapolation; optimum choice of relaxation factor; convergence acceleration; successive overrelaxation; iterative process; S.O.R. method; two step extrapolation; optimum choice of relaxation factor; convergence acceleration; successive overrelaxation},
language = {eng},
number = {3},
pages = {177-196},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Two step extrapolation and optimum choice of relaxation factor of the extrapolated S.O.R. method},
url = {http://eudml.org/doc/15536},
volume = {33},
year = {1988},
}

TY - JOUR
AU - Zítko, Jan
TI - Two step extrapolation and optimum choice of relaxation factor of the extrapolated S.O.R. method
JO - Aplikace matematiky
PY - 1988
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 33
IS - 3
SP - 177
EP - 196
AB - Limits of the extrapolation coefficients are rational functions of several poles with the largest moduli of the resolvent operator $R(\lambda , T)=(\lambda I -T)^{-1}$ and therefore good estimates of these poles could be calculated from these coefficients. The calculation is very easy for the case of two coefficients and its practical effect in finite dimensional space is considerable. The results are used for acceleration of S.O.R. method.
LA - eng
KW - two step extrapolation; optimum choice of relaxation factor; convergence acceleration; successive overrelaxation; iterative process; S.O.R. method; two step extrapolation; optimum choice of relaxation factor; convergence acceleration; successive overrelaxation
UR - http://eudml.org/doc/15536
ER -

## References

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1. J. Zítko, Improving the convergence of iterative methods, Apl. Mat. 28 (1983), 215-229. (1983) MR0701740
2. J. Zítko, Convergence of extrapolation coefficients, Apl. Mat. 29 (1984), 114-133. (1984) MR0738497
3. J. Zítko, Extrapolation of iterative processes, Rostock. Math. Kolloq. 25, 63-78 (1984). (1984) MR0763678
4. I. Marek J. Zítko, Ljusternik acceleration and the extrapolated S.O.R. method, Appl. Mat. 22 (1977), 116-133. (1977) MR0431667
5. A. E. Taylor, Introduction to Functional Analysis, J. Wiley Publ. New-York 1958. (1958) Zbl0081.10202MR0098966
6. D. M. Young, Iterative Solution of Large Linear Systems, Academic Press, New York- London, 1971. (1971) Zbl0231.65034MR0305568
7. R. S. Varga, Matrix Iterative Analysis, Prentice-Hall, Englewood Cliffs, New Jersey 1962. (1962) MR0158502
8. G. Maess, 10.1002/zamm.19760560210, ZAMM 56 (1976), 121-122. (1976) MR0426417DOI10.1002/zamm.19760560210
9. G. Maess, Iterative Lösung linearer Gleichungssysteme, Deutsche Akademie der Naturforscher Leopoldina Halle (Saale), 1979. (1979) Zbl0416.65029MR0558164

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