| Title:
|
On determination of eigenvalues and eigenvectors of selfadjoint operators (English) |
| Author:
|
Kolomý, Josef |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
26 |
| Issue:
|
3 |
| Year:
|
1981 |
| Pages:
|
161-170 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
Two simple methods for approximate determination of eigenvalues and eigenvectors of linear self-adjoint operators are considered in the following two cases: (i) lower-upper bound $\lambda _1$ of the spectrum $\sigma (A)$ of $A$ is an isolated point of $\sigma (A)$; (ii) $\lambda _1$ (not necessarily an isolated point of $\sigma (A)$ with finite multiplicity) is an eigenvalue of $A$. (English) |
| Keyword:
|
eigenvalues |
| Keyword:
|
eigenvectors |
| Keyword:
|
self-adjoint operators |
| Keyword:
|
spectrum |
| MSC:
|
47A10 |
| MSC:
|
47A70 |
| MSC:
|
47B25 |
| MSC:
|
49G20 |
| MSC:
|
65J10 |
| idZBL:
|
Zbl 0469.65033 |
| idMR:
|
MR0615603 |
| DOI:
|
10.21136/AM.1981.103908 |
| . |
| Date available:
|
2008-05-20T18:16:46Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103908 |
| . |
| Reference:
|
[1] R. I. Andrushkiw: On the approximate solution of K-positive eigenvalue problems $T(u) - \lambda S(u) = 0$.J. Math. Anal. Appl. 50 (1975), 511 -527. MR 0390817, 10.1016/0022-247X(75)90007-4 |
| Reference:
|
[2] И. А. Биргер: Некоторые математические методы решения инженерных задач.Изд. Оборонгиз (Москва, 1956). Zbl 0995.90522 |
| Reference:
|
[3] H. Bückner: An iterative method for solving nonlinear integral equations.Symp. on the numerical treatment of ordinary differential equations, integral and integro-differential equations, 613 - 643, Roma 1960, Birkhäuser Verlag, Basel- Stuttgart, 1960. MR 0129571 |
| Reference:
|
[4] J. Kolomý: On convergence of the iteration methods.Comment. Math. Univ. Carolinae 1 (1960), 18-24. |
| Reference:
|
[5] J. Kolomý: On the solution of homogeneous functional equations in Hilbert space.Comment. Math. Univ. Carolinae 3 (1962), 36-47. MR 0149306 |
| Reference:
|
[6] J. Kolomý: Approximate determination of eigenvalues and eigenvectors of self-adjoint operators.Ann. Math. Pol. 38 (1980), 153 - 158. MR 0599239, 10.4064/ap-38-2-153-158 |
| Reference:
|
[7] J. Kolomý: Some methods for finding of eigenvalues and eigenvectors of linear and nonlinear operators.Abhandlungen der DAW, Abt. Math. Naturwiss. Tech., 1978, 6, 159-166, Akademie-Verlag, Berlin, 1978. MR 0540456 |
| Reference:
|
[8] M. А. Красносельский, другие: Приближенное решение операторных уравнений.Наука (Москва, 1969). Zbl 1149.62317 |
| Reference:
|
[9] I. Marek: Iterations of linear bounded operators in non self-adjoint eigenvalue problems and Kellogg's iteration process.Czech. Math. Journal 12 (1962), 536-554. Zbl 0192.23701, MR 0149297 |
| Reference:
|
[10] I. Marek: Kellogg's iteration with minimizing parameters.Comment. Math. Univ. Carolinae 4 (1963), 53-64. MR 0172459 |
| Reference:
|
[11] Г. И. Марчук: Методы вычислительной математили.Изд. Наука (Новосибирск, 1973). Zbl 1170.01397 |
| Reference:
|
[12] W. V. Petryshyn: On the eigenvalue problem $T(u) - \lambda S(u) = 0$ with unbounded and symmetric operators T and S.Phil. Trans. of the Royal Soc. of London, Ser. A. Math. and Phys. Sciences No 1130, Vol. 262 (1968), 413-458. MR 0222697 |
| Reference:
|
[13] А. И. Плеснер: Спектральная теория линейных операторов.Изд. Наука (Москва, 1965). Zbl 1099.01519 |
| Reference:
|
[14] Wang Jin-Ru (Wang Chin-Ju): Gradient methods for finding eigenvalues and eigenvectors.Chinese Math. - Acta 5 (1964), 578-587. MR 0173358 |
| Reference:
|
[15] A. E. Taylor: Introduction in Functional Analysis.J. Wiley and Sons, Inc., New York, 1967. |
| . |
