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Monotone convergence theorems for variational triples with applications to intermediate problems

Published online by Cambridge University Press:  14 November 2011

R. D. Brown
R. D. Brown
Affiliation:
Department of Mathematics, University of Kansas, Lawrence, Kansas 66045, U.S.A
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Synopsis

The variational eigenvalue problem for a real quadratic form b with respect to a positive definite form a on a vector space V may be represented by the triple (b, a, V). Methods of intermediate problems provide approximations from below to the lower eigenvalues of (b, a, V) using monotone increasing sequences of such triples. It is shown that every such approximation method is canonically equivalent to Weinstein's method. General convergence theorems are proved for such methods. These results generalise known convergence results for increasing sequences of quadratic forms. The results are applied to some specific approximation methods and are illustrated using a differential eigenvalue problem.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 117 , Issue 1-2 , 1991 , pp. 39 - 58
Copyright
Copyright © Royal Society of Edinburgh 1991

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