Title:

Ljusternik acceleration and the extrapolated S.O.R. method (English) 
Author:

Marek, Ivo 
Author:

Zítko, Jan 
Language:

English 
Journal:

Aplikace matematiky 
ISSN:

03736725 
Volume:

22 
Issue:

2 
Year:

1977 
Pages:

116133 
Summary lang:

English 
Summary lang:

Czech 
Summary lang:

Russian 
. 
Category:

math 
. 
Summary:

A general semiiterative 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:

20080520T18:06:44Z 
Last updated:

20200728 
Stable URL:

http://hdl.handle.net/10338.dmlcz/103683 
. 
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), 4964 (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 RadonNikolskii operators and their generalizations.Comment. Math. Univ. Carol. 3. (1962), N1, 2030. 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), 7289. MR 0381270 
. 