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Title: Ljusternik acceleration and the extrapolated S.O.R. method (English)
Author: Marek, Ivo
Author: Zítko, Jan
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 22
Issue: 2
Year: 1977
Pages: 116-133
Summary lang: English
Summary lang: Czech
Summary lang: Russian
Category: math
Summary: A general semi-iterative acceleration technique is described for improving the convergence of stationary iterative methods. By applying this technique to the successive over relaxation (S.O.R.) iterations with a particular nonoptimal relaxation factor an acceleration of the rate of convergence is obtained which is superior to the optimal S.O.R. ()
MSC: 65F10
MSC: 65F15
MSC: 65J05
MSC: 65N22
idZBL: Zbl 0367.65016
idMR: MR0431667
DOI: 10.21136/AM.1977.103683
Date available: 2008-05-20T18:06:44Z
Last updated: 2020-07-28
Stable URL:
Reference: [1] L. A. Ljusternik: A note for the numerical solution of boundary value problems for the Laplace equation and for the calculation of eigenvalues by the method of nets.Trudy Inst. Math. Academy of Sciences of the USSR, 20 (1947), 49-64 (Russian). MR 0025825
Reference: [2] I. Marek: On a method of accelerating the convergence of iterative processes.Journal Соmр. Math. and Math. Phys. 2 (1962), N 2, 963 - 971 (Russian). MR 0152112
Reference: [3] I. Marek: On Ljusternik's method of improving the convergence of nonlinear iterative sequences.Comment. Math. Univ. Carol, 6 (1965), N3, 371 - 380. MR 0196901
Reference: [4] I. Marek: On some spectral properties of Radon-Nikolskii operators and their generalizations.Comment. Math. Univ. Carol. 3. (1962), N1, 20-30. MR 0144216
Reference: [5] A. E. Taylor: Introduction to Functional Analysis.J. Wiley Publ. New York, 1958. Zbl 0081.10202, MR 0098966
Reference: [6] D. M. Young: Iterative Solution of Large Linear Systems.Academic Press, New York - London, 1971. Zbl 0231.65034, MR 0305568
Reference: [7] J. Zítko: Extrapolation of S.O.R. iterations.Apl. Mat. 19 (1974), 72-89. MR 0381270


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