Local two-sided bounds for eigenvalues of self-adjoint operators

Lyonell Boulton; Gabriel Barrenechea; Nabile Boussaid

doi:10.1007/s00211-016-0822-1

Local two-sided bounds for eigenvalues of self-adjoint operators

Lyonell Boulton, Gabriel Barrenechea, Nabile Boussaid

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Abstract

We examine the equivalence between an extension of the Lehmann-Maehly-Goerisch method developed a few years ago by Zimmermann andMertins, and a geometrically motivated method developed more recently byDavies and Plum. We establish a general framework which allows sharpeningvarious previously known results in these two settings and determine explicitconvergence estimates for both methods. We demonstrate the applicability ofthe method of Zimmermann and Mertins by means of numerical tests on theresonant cavity problem.

Original language	English
Journal	Numerische Mathematik
Early online date	9 Jul 2016
DOIs	https://doi.org/10.1007/s00211-016-0822-1
Publication status	E-pub ahead of print - 9 Jul 2016

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Lyonell Boulton
- l.boulton@hw.ac.uk
- School of Mathematical & Computer Sciences - Professor
- School of Mathematical & Computer Sciences, Mathematics - Professor
Person: Academic (Research & Teaching)

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AU - Boussaid, Nabile

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N2 - We examine the equivalence between an extension of the Lehmann-Maehly-Goerisch method developed a few years ago by Zimmermann andMertins, and a geometrically motivated method developed more recently byDavies and Plum. We establish a general framework which allows sharpeningvarious previously known results in these two settings and determine explicitconvergence estimates for both methods. We demonstrate the applicability ofthe method of Zimmermann and Mertins by means of numerical tests on theresonant cavity problem.

AB - We examine the equivalence between an extension of the Lehmann-Maehly-Goerisch method developed a few years ago by Zimmermann andMertins, and a geometrically motivated method developed more recently byDavies and Plum. We establish a general framework which allows sharpeningvarious previously known results in these two settings and determine explicitconvergence estimates for both methods. We demonstrate the applicability ofthe method of Zimmermann and Mertins by means of numerical tests on theresonant cavity problem.

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DO - 10.1007/s00211-016-0822-1

M3 - Article

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JO - Numerische Mathematik

JF - Numerische Mathematik

SN - 0029-599X

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Local two-sided bounds for eigenvalues of self-adjoint operators

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Lyonell Boulton

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