Geodesic
Ljusternik acceleration and the extrapolated S.O.R. method
Applications of Mathematics, Tome 22 (1977) no. 2, pp. 116-133
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
DOI : 10.21136/AM.1977.103683
Classification : 65F10, 65F15, 65J05, 65N22 
@article{10_21136_AM_1977_103683,
     author = {Marek, Ivo and Z{\'\i}tko, Jan},
     title = {Ljusternik acceleration and the extrapolated {S.O.R.} method},
     journal = {Applications of Mathematics},
     pages = {116--133},
     year = {1977},
     volume = {22},
     number = {2},
     doi = {10.21136/AM.1977.103683},
     mrnumber = {0431667},
     zbl = {0367.65016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1977.103683/}
}
TY  - JOUR
AU  - Marek, Ivo
AU  - Zítko, Jan
TI  - Ljusternik acceleration and the extrapolated S.O.R. method
JO  - Applications of Mathematics
PY  - 1977
SP  - 116
EP  - 133
VL  - 22
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1977.103683/
DO  - 10.21136/AM.1977.103683
LA  - en
ID  - 10_21136_AM_1977_103683
ER  - 
%0 Journal Article
%A Marek, Ivo
%A Zítko, Jan
%T Ljusternik acceleration and the extrapolated S.O.R. method
%J Applications of Mathematics
%D 1977
%P 116-133
%V 22
%N 2
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1977.103683/
%R 10.21136/AM.1977.103683
%G en
%F 10_21136_AM_1977_103683
Marek, Ivo; Zítko, Jan. Ljusternik acceleration and the extrapolated S.O.R. method. Applications of Mathematics, Tome 22 (1977) no. 2, pp. 116-133. doi: 10.21136/AM.1977.103683

[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

[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

[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

[4] I. Marek: On some spectral properties of Radon-Nikolskii operators and their generalizations. Comment. Math. Univ. Carol. 3. (1962), N1, 20-30. | MR

[5] A. E. Taylor: Introduction to Functional Analysis. J. Wiley Publ. New York, 1958. | MR | Zbl

[6] D. M. Young: Iterative Solution of Large Linear Systems. Academic Press, New York - London, 1971. | MR | Zbl

[7] J. Zítko: Extrapolation of S.O.R. iterations. Apl. Mat. 19 (1974), 72-89. | MR

Cité par Sources :