# Convergence of approximation methods for eigenvalue problem for two forms

Aplikace matematiky (1984)

- Volume: 29, Issue: 5, page 333-341
- ISSN: 0862-7940

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topRegińska, Teresa. "Convergence of approximation methods for eigenvalue problem for two forms." Aplikace matematiky 29.5 (1984): 333-341. <http://eudml.org/doc/15364>.

@article{Regińska1984,

abstract = {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.},

author = {Regińska, Teresa},

journal = {Aplikace matematiky},

keywords = {external approximation; eigenvalue problem; bilinear forms; spectral approximation; convergence; external approximation; eigenvalue problem; bilinear forms; spectral approximation; convergence},

language = {eng},

number = {5},

pages = {333-341},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Convergence of approximation methods for eigenvalue problem for two forms},

url = {http://eudml.org/doc/15364},

volume = {29},

year = {1984},

}

TY - JOUR

AU - Regińska, Teresa

TI - Convergence of approximation methods for eigenvalue problem for two forms

JO - Aplikace matematiky

PY - 1984

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 29

IS - 5

SP - 333

EP - 341

AB - 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.

LA - eng

KW - external approximation; eigenvalue problem; bilinear forms; spectral approximation; convergence; external approximation; eigenvalue problem; bilinear forms; spectral approximation; convergence

UR - http://eudml.org/doc/15364

ER -

## References

top- 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. (1951) MR0044736
- R. D. Brown, 10.1216/RMJ-1980-10-1-199, Rocky Mt. J. of Math. 10, No. 1, 1980, 199 - 215. (1980) Zbl0445.49043MR0573871DOI10.1216/RMJ-1980-10-1-199
- N. Dunford J. T. Schwartz, Linear Operators, Spectral Theory, New York, Irterscience 1963. (1963) MR0188745
- T. Kato, Perturbation Theory for Linear Operators, Sprirger Verlag, Berlin 1966. (1966) Zbl0148.12601
- T. Regińska, External approximation of eigenvalue problems in Banach spaces, RAFRO Numerical Analysis, 1984. (1984) MR0743883
- F. Stummel, 10.1007/BF01349967, Math. Ann. 190, 1970, 45 - 92: II. Math. Z. 120, 1971, 231-264. (190,) MR0291870DOI10.1007/BF01349967
- H. F. Weinberger, Variational methods for eigenvalue approximation, Reg. Conf. Series in appl. math. 15, 1974. (1974) Zbl0296.49033MR0400004

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