Abstract
It is well known that the standard projection methods allow one to recover the whole spectrum of a bounded self-adjoint operator but they often lead to spectral pollution, i.e. to spurious eigenvalues lying in the gaps of the essential spectrum. Methods using second order relative spectra are free from spectral pollution, but they have not been proven to approximate the whole spectrum. L. Boulton ([3] and [4]) has shown that second order relative spectra approximate all isolated eigenvalues of finite multiplicity. The main result of the present paper is that second order relative spectra do not in general approximate the whole of the essential spectrum of a bounded self-adjoint operator.
Original language | English |
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Pages (from-to) | 535-552 |
Number of pages | 18 |
Journal | Journal of Spectral Theory |
Volume | 3 |
Issue number | 4 |
Early online date | 21 Mar 2012 |
DOIs | |
Publication status | Published - 1 Jan 2013 |
Keywords
- Projection methods
- Second order relative spectra
- Self-adjoint operators