Spectral pollution

@inproceedings{Davies2002SpectralP,
  title={Spectral pollution},
  author={E. B. Davies and Michael Plum},
  year={2002}
}
M. PLUM Mathematisches Institut I, Universität Karlsruhe, Kaiserstrasse 12, D-76128 Karlsruhe, Germany [Received on 10 December 2002; revised on 12 January 2004] It is well known that routine methods of computing the spectrum of a self-adjoint operator often lead to spurious eigenvalues in a gap between two parts of the essential spectrum. We provide a geometrical explanation for a numerical method of resolving this problem, and give some examples of its use. 
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