| Title:
|
Convergence of approximation methods for eigenvalue problem for two forms (English) |
| Author:
|
Regińska, Teresa |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
29 |
| Issue:
|
5 |
| Year:
|
1984 |
| Pages:
|
333-341 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper concerns an approximation of an eigenvalue problem for two forms on a Hilbert space $X$. We investigate some approximation methods generated by sequences of forms $a_n$ and $b_n$ defined on a dense subspace of $X$. The proof of convergence of the methods is based on the theory of the external approximation of eigenvalue problems. The general results are applied to Aronszajn's method. (English) |
| Keyword:
|
external approximation |
| Keyword:
|
eigenvalue problem |
| Keyword:
|
bilinear forms |
| Keyword:
|
spectral approximation |
| Keyword:
|
convergence |
| MSC:
|
35P15 |
| MSC:
|
47A10 |
| MSC:
|
47A55 |
| MSC:
|
47A70 |
| MSC:
|
49G15 |
| MSC:
|
65F15 |
| MSC:
|
65J10 |
| idZBL:
|
Zbl 0584.65033 |
| idMR:
|
MR0772268 |
| DOI:
|
10.21136/AM.1984.104103 |
| . |
| Date available:
|
2008-05-20T18:25:38Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104103 |
| . |
| Reference:
|
[1] N. Aronszajn: Approximation methods for eigenvalues of completely continuous symmetric operator.Proc. of Symposium on Spectral Theory and Differential Equations, Stillwater, Oklahoma, 1951, 179-202. MR 0044736 |
| Reference:
|
[2] R. D. Brown: Convergence of approximation methods for eigenvalues of completely continuous quadratic forms.Rocky Mt. J. of Math. 10, No. 1, 1980, 199 - 215. Zbl 0445.49043, MR 0573871, 10.1216/RMJ-1980-10-1-199 |
| Reference:
|
[3] N. Dunford J. T. Schwartz: Linear Operators, Spectral Theory.New York, Irterscience 1963. MR 0188745 |
| Reference:
|
[4] T. Kato: Perturbation Theory for Linear Operators.Sprirger Verlag, Berlin 1966. Zbl 0148.12601 |
| Reference:
|
[5] T. Regińska: External approximation of eigenvalue problems in Banach spaces.RAFRO Numerical Analysis, 1984. MR 0743883 |
| Reference:
|
[6] F. Stummel: Diskrete Konvergenz linear Operatoren, I.Math. Ann. 190, 1970, 45 - 92: II. Math. Z. 120, 1971, 231-264. MR 0291870, 10.1007/BF01349967 |
| Reference:
|
[7] H. F. Weinberger: Variational methods for eigenvalue approximation.Reg. Conf. Series in appl. math. 15, 1974. Zbl 0296.49033, MR 0400004 |
| . |
