Non-variational approximation of discrete eigenvalues of self-adjoint operators

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Abstract

We establish sufficient conditions for approximation of discrete eigenvalues of self-adjoint operators in the second-order projection method suggested recently in Levitin & Shargorodsky (2004, Spectral pollution and second order relative spectra for self-adjoint operators. IMA J. Numer. Anal., 24, 393-416). We find fairly explicit estimates for the eigenvalue error and study in detail two concrete model examples. Our results show that second-order projection strategies not only are universally pollution free but also achieve approximation under natural conditions on the discretising basis. © The author 2006.

Original languageEnglish
Pages (from-to)102-121
Number of pages20
JournalIMA Journal of Numerical Analysis
Volume27
Issue number1
DOIs
Publication statusPublished - Jan 2007

Keywords

  • Non-variational projection methods
  • Numerical approximation of the spectrum
  • Spectral pollution

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