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

被引：3

作者：

Barrenechea, G. R. ^{[1
]}

Boulton, L. ^{[2
,3
]}

Boussaid, N. ^{[4
]}

机构：

[1] Univ Strathclyde, Dept Math & Stat, 26 Richmond St, Glasgow G1 1XH, Lanark, Scotland

[2] Heriot Watt Univ, Dept Math, Edinburgh EH14 4AS, Midlothian, Scotland

[3] Heriot Watt Univ, Maxwell Inst Math Sci, Edinburgh EH14 4AS, Midlothian, Scotland

[4] Univ Franche Comte, UFR Sci & Tech, Math Lab, 16 Route Gray, F-25030 Besancon, France

来源：

NUMERISCHE MATHEMATIK | 2017年 / 135卷 / 04期

基金：

英国工程与自然科学研究理事会;

关键词：

ELEMENT APPROXIMATION; ENCLOSURES;

D O I：

10.1007/s00211-016-0822-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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

引用

页码：953 / 986

页数：34

共 50 条

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[2] BOUNDS FOR EIGENVALUES OF SELF-ADJOINT OPERATORS
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[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 1970, 7 (03) : 458 - &
[3] METHODS FOR COMPUTING LOWER BOUNDS TO EIGENVALUES OF SELF-ADJOINT OPERATORS
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[4] INEQUALITIES FOR EIGENVALUES OF SELF-ADJOINT OPERATORS
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[9] OBSERVATIONS ON THE STABILITY OF THE EIGENVALUES OF SELF-ADJOINT OPERATORS
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[10] AN INEQUALITY FOR EIGENVALUES OF A CLASS OF SELF-ADJOINT OPERATORS
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