| Title:
|
Kellogg's iterations for general complex matrix (English) |
| Author:
|
Zítko, Jan |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
19 |
| Issue:
|
5 |
| Year:
|
1974 |
| Pages:
|
342-365 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $A$ be a nonzero complex matrix $n \times n, x_0\in V_n(C), x_0\neq\Theta$. Let us define $x_k=A^kx_0$, $\mu_k=x^H_kx_k/x^H_{k-1}x_{k-1}$ and $v_k=x^H_{k-1}x_k/x^H_{k-1}x_{k-1}$. In this paper, assymptotic behaviour of the numbers $\mu_k$ and $v_k$ is studied in detail, mainly for matrices with nonlinear elementary divisors. () |
| MSC:
|
15A18 |
| MSC:
|
65B05 |
| MSC:
|
65F15 |
| idZBL:
|
Zbl 0315.65025 |
| idMR:
|
MR0368406 |
| DOI:
|
10.21136/AM.1974.103550 |
| . |
| Date available:
|
2008-05-20T17:59:48Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103550 |
| . |
| Reference:
|
[1] A. S. Householder: The Theory of Matrices in Numerical Analysis.Blaisdell Publishing Company 1965. MR 0175290 |
| Reference:
|
[2] A. Ralston: A First Course in Numerical Analysis.Mc Graw-Hill Book Company, 1965. Zbl 0139.31603, MR 0191070 |
| Reference:
|
[3] R. S. Vargа: Matrix Iterative Analysis.Prentice-Hall, Englewood Cliffs, New Jersey, 1962. MR 0158502 |
| Reference:
|
[4] V. Jarník: Differential Calculus II.(in Czech). Nakladatelství ČSAV, Praha 1956. |
| Reference:
|
[5] I. Marek: Iterations of Linear Bounded Operators in Non Self-Adjoint Eigenvalue Problems and Kellogg's Iteration Process.Czech. Math. Journal, 12 (87), 536-554, Prague. Zbl 0192.23701 |
| Reference:
|
[6] O. D. Kellogg: On the existence and closure of sets of characteristic functions.Math. Annalen, Band 86, Berlin 1922. |
| Reference:
|
[7] F. Riesz B. Nagy: Lecons d'analyse fonctionelle.Budapest 1953. |
| . |
