On the convergence of second-order spectra and multiplicity

L. Boulton; M. Strauss

doi:10.1098/rspa.2010.0233

On the convergence of second-order spectra and multiplicity

L. Boulton, M. Strauss

Mathematics And Statistics

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

10 Citations (Scopus)

Abstract

The notion of second-order relative spectrum of a self-adjoint operator acting on a Hilbert space has been studied recently in connection with the phenomenon of spectral pollution in the Galerkin method. In this paper we examine how the second-order spectrum encodes precise information about the multiplicity of the isolated eigenvalues of the underlying operator. Our theoretical findings are supported by various numerical experiments on the computation of guaranteed eigenvalue inclusions via finite element bases.

Original language	English
Pages (from-to)	264-284
Number of pages	21
Journal	Proceedings A: Mathematical, Physical and Engineering Sciences
Volume	467
Issue number	2125
DOIs	https://doi.org/10.1098/rspa.2010.0233
Publication status	Published - 2011

Keywords

self-adjoint operators
approximation
spectral exactness
second-order spectrum
Eigen values
pollution
projection methods
spectral pollution
relative spectra

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10.1098/rspa.2010.0233

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1 Finished

Spectral Theory of Block Operator Matrices
Langer, M.
EPSRC (Engineering and Physical Sciences Research Council)
1/09/07 → 30/11/09
Project: Research

Cite this

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KW - self-adjoint operators

KW - approximation

KW - spectral exactness

KW - second-order spectrum

KW - Eigen values

KW - pollution

KW - projection methods

KW - spectral pollution

KW - relative spectra

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JF - Proceedings A: Mathematical, Physical and Engineering Sciences

SN - 1364-5021

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On the convergence of second-order spectra and multiplicity

Abstract

Keywords

Access to Document

Spectral Theory of Block Operator Matrices

Cite this