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

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

33 Downloads (Pure)

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

Access to Document

10.1007/s00211-016-0822-1

Download pdfFinal published version, 867 KBLicence: CC BY

Fingerprint Dive into the research topics of 'Local two-sided bounds for eigenvalues of self-adjoint operators'. Together they form a unique fingerprint.

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

Cite this

@article{2bed853c93a54e4bbf6ee4714ad3a1ad,

title = "Local two-sided bounds for eigenvalues of self-adjoint operators",

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.",

author = "Lyonell Boulton and Gabriel Barrenechea and Nabile Boussaid",

year = "2016",

month = jul,

day = "9",

doi = "10.1007/s00211-016-0822-1",

language = "English",

journal = "Numerische Mathematik",

issn = "0029-599X",

publisher = "Springer",

}

TY - JOUR

T1 - Local two-sided bounds for eigenvalues of self-adjoint operators

AU - Boulton, Lyonell

AU - Barrenechea, Gabriel

AU - Boussaid, Nabile

PY - 2016/7/9

Y1 - 2016/7/9

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.

U2 - 10.1007/s00211-016-0822-1

DO - 10.1007/s00211-016-0822-1

M3 - Article

C2 - 28615746

JO - Numerische Mathematik

JF - Numerische Mathematik

SN - 0029-599X

ER -