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.
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