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A hierarchical method for obtaining eigenvalue enclosures

Author: E. B. Davies
Journal: Math. Comp. 69 (2000), 1435-1455
MSC (1991): Primary 34L15, 35P15, 49R05, 49R10, 65L15, 65L60, 65L70, 65N25
Published electronically: March 6, 2000
MathSciNet review: 1710648
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Abstract | References | Similar Articles | Additional Information


We introduce a new method of obtaining guaranteed enclosures of the eigenvalues of a variety of self-adjoint differential and difference operators with discrete spectrum. The method is based upon subdividing the region into a number of simpler regions for which eigenvalue enclosures are already available.

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Additional Information

E. B. Davies
Affiliation: Department of Mathematics, King’s College, Strand, London, WC2R 2LS, United Kingdom

Keywords: Spectrum, eigenvalues, spectral enclosures, interval arithmetic, Rayleigh-Ritz method, Temple-Lehmann method
Received by editor(s): October 27, 1998
Published electronically: March 6, 2000
Article copyright: © Copyright 2000 American Mathematical Society