Spectral pollution and second-order relative spectra for self-adjoint operators

@article{Levitin2002SpectralPA,
  title={Spectral pollution and second-order relative spectra for self-adjoint operators},
  author={Michael Levitin and Eugene Shargorodsky},
  journal={Ima Journal of Numerical Analysis},
  year={2002},
  volume={24},
  pages={393-416}
}
We consider the phenomenon of spectral pollution arising in calculation of spectra of self-adjoint operators by projection methods. We suggest a strategy of dealing with spectral pollution by using the so-called second-order relative spectra. The effectiveness of the method is illustrated by a detailed analysis of two model examples. 
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