| Title:
|
Zrychlování konvergence lineárních iteračních procesů v Banachových prostorech (Czech) |
| Title:
|
Convergence acceleration of linear iterative processes in Banach spaces (English) |
| Author:
|
Kovářík, Zdislav |
| Language:
|
Czech |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
11 |
| Issue:
|
4 |
| Year:
|
1966 |
| Pages:
|
266-270 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
The convergence of the sequence $x_{n+1}=Ax_n+b$ to $(l-A)^{-1}b$ (where $x_n, b$ are vectors in Banach space, $A$ is a bounded linear operator with bounded $(l-A)^{-1}$) can be accelerated by constructing certain linear combinations of several ordinary successive approximations. A sufficient condition is that the spectrum of $A$ decompose into a finite set and a subset of a sufficiently small neighborhood of zero (e. g., $A$ is compact). (English) |
| Keyword:
|
numerical analysis |
| MSC:
|
65.10 |
| idZBL:
|
Zbl 0154.16802 |
| idMR:
|
MR0203903 |
| DOI:
|
10.21136/AM.1966.103028 |
| . |
| Date available:
|
2008-05-20T17:35:52Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103028 |
| . |
| Reference:
|
[1] D. K. Faddějev V. N. Faddějevová: Numerické metody lineární algebry;.SNTL, Praha 1964 (překlad z ruštiny). |
| Reference:
|
[2] И. С. Березин H. П. Жидков: Методы вычислений, т. II;.ФИЗМАТГИЗ, Москва 1962. Zbl 0285.34022 |
| Reference:
|
[3] H. Данфорд, Дж. Шварц: Линейные операторы.(общая теория); ИИЛ, Москва 1962 (перевод с английского). Zbl 1005.68507 |
| . |
