On the convergence of second-order spectra and multiplicity

Lyonell Boulton, Michael Strauss

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10 Citations (Scopus)


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. © 2011 The Royal Society.

Original languageEnglish
Pages (from-to)264-284
Number of pages21
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2125
Publication statusPublished - 8 Jan 2011


  • Second-order spectrum
  • Spectral exactness
  • Spectral pollution


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