| Title:
|
Extrapolation of S. O. R. iterations (English) |
| Author:
|
Zítko, Jan |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
19 |
| Issue:
|
2 |
| Year:
|
1974 |
| Pages:
|
72-89 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the paper, the system of $n$ linear algebraic equations $Ax=b$ with 2-cyclic matrix is considered. Methods are derived which converge to the solution $x$ faster than the optimal successive overrelaxation iterative method. () |
| MSC:
|
65B05 |
| MSC:
|
65F10 |
| MSC:
|
65J05 |
| idZBL:
|
Zbl 0293.65020 |
| idMR:
|
MR0381270 |
| DOI:
|
10.21136/AM.1974.103516 |
| . |
| Date available:
|
2008-05-20T17:58:15Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103516 |
| . |
| Reference:
|
[1] A. S. Householder: The Theory of Matrices in Numerical Analysis.Blaisdell Publishing Company 1965. MR 0175290 |
| Reference:
|
[2] D. K. Faddějev, V. N. Faddějevová: Numerical Methods in Linear Algebra.(Numerické metody lineární algebry). SNTL, Praha 1964. |
| Reference:
|
[3] A. Ralston: A First Course in Numerical Analysis.McGraw-Hill Book Company, 1965. Zbl 0139.31603, MR 0191070 |
| Reference:
|
[4] R. S. Varga: Matrix Iterative Analysis.Prentice-Hall, Englewood Cliffs, New Jersey 1962. MR 0158502 |
| Reference:
|
[5] G. J. Tee: Eigenvectors of the Successive Overrelaxation Process and its Combination with Chebyshev Semi-Iteration.The Computer Journal, Vol. 6, No 3, October 1963, str. 250-263. 10.1093/comjnl/6.3.250 |
| Reference:
|
[6] D. M. Young: Iterative Method for Solving Partial Difference Equation of Elliptic Type.Trans. Amer. Math. Soc. 76, 1954, 92-111. MR 0059635, 10.1090/S0002-9947-1954-0059635-7 |
| Reference:
|
[7] E. Humhal J. Zítko: Contribution to the S.O.R. Method.(Poznámka k superrelaxační metodě). Aplikace matematiky 3, sv. 12, 1967, 161 - 170. MR 0224263 |
| Reference:
|
[8] Л. А. Люстерник: Замечания к численному решению краевых задач уравнения Лапласа и вычислениям собственных значений методом сеток.Tp. Матем. института АН СССР, 1947, 20, 49-64. Zbl 1153.11318, MR 0025825 |
| Reference:
|
[9] I. Marek: On Ljusternik's Method of Improving Convergence of Nonlinear Iterative Sequences.CMUC 6, 3, 1965, 371-380. MR 0196901 |
| Reference:
|
[10] И. Марек: Об одном методе ускорения сходимости итерационных процесов.ЖВМиМФ, Том 2, Но 6, 1962, 963-971. Zbl 1005.68507, MR 0152112 |
| Reference:
|
[11] С. G. Broyden: Some Generalizations of the Theory of Successive Over-Relaxation.Numer. Math. 6, Heft 4, 1964, 269-284. MR 0171378, 10.1007/BF01386075 |
| Reference:
|
[12] L. A. Hageman R. B. Kellogg: Estimating Optimum Overrelaxation Parameter.Math. of Соmр., January 1968, Vol. 22, No 101, 60-68. MR 0229371 |
| . |
