Article
MSC:
35P15,
47A10,
47A55,
47A70,
49G15,
65F15,
65J10 | MR 0772268 | Zbl 0584.65033 | DOI: 10.21136/AM.1984.104103
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Keywords:
external approximation; eigenvalue problem; bilinear forms; spectral approximation; convergence
external approximation; eigenvalue problem; bilinear forms; spectral approximation; convergence
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.
References:
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[4] T. Kato: Perturbation Theory for Linear Operators. Sprirger Verlag, Berlin 1966. Zbl 0148.12601
[5] T. Regińska: External approximation of eigenvalue problems in Banach spaces. RAFRO Numerical Analysis, 1984. MR 0743883
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[7] H. F. Weinberger: Variational methods for eigenvalue approximation. Reg. Conf. Series in appl. math. 15, 1974. MR 0400004 | Zbl 0296.49033
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