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On the convergence of second-order spectra and multiplicity

Boulton, L. and Strauss, M. (2011) On the convergence of second-order spectra and multiplicity. Proceedings A: Mathematical, Physical and Engineering Sciences, 467 (2125). pp. 264-284. ISSN 1364-5021

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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.

Item type: Article
ID code: 40412
Keywords: self-adjoint operators, approximation, spectral exactness, second-order spectrum, Eigen values, pollution, projection methods, spectral pollution, relative spectra, Probabilities. Mathematical statistics
Subjects: Science > Mathematics > Probabilities. Mathematical statistics
Department: Faculty of Science > Mathematics and Statistics
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Depositing user: Pure Administrator
Date Deposited: 17 Jul 2012 11:21
Last modified: 27 Mar 2014 10:16
URI: http://strathprints.strath.ac.uk/id/eprint/40412

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