Non-variational approximation of discrete eigenvalues of self-adjoint operators |
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Authors: | Boulton Lyonell |
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Institution: |
Department of Mathematics, Heriot-Watt University, Edinburgh EH14 2AS, UK
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Abstract: | ** Email: L.Boulton{at}ma.hw.ac.uk
We establish sufficient conditions for approximation of discreteeigenvalues of self-adjoint operators in the second-order projectionmethod suggested recently in Levitin & Shargorodsky (2004,Spectral pollution and second order relative spectra for self-adjointoperators. IMA J. Numer. Anal., 24, 393416). We findfairly explicit estimates for the eigenvalue error and studyin detail two concrete model examples. Our results show thatsecond-order projection strategies not only are universallypollution free but also achieve approximation under naturalconditions on the discretising basis. |
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Keywords: | non-variational projection methods spectral pollution numerical approximation of the spectrum |
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