Geodesic
Computation of the eigenvalues of a discrete selfadjoint operator perturbed by a bounded operator
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2008), pp. 16-24.

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We generalize the method of regularized traces which calculates eigenvalues of a perturbed discrete operator for the case of an arbitrary multiplicity of eigenvalues of the unperturbed operator. We obtain a system of equations, enabling one to calculate eigenvalues of the perturbed operator with large ordinal numbers. As an example, we calculate eigenvalues of a perturbed Laplace operator in a rectangle.
Keywords: a discrete self-adjoint operator, a separable Hilbert space, eigenvalues and eigenfunctions of an operator, a regularized trace, errors in the perturbation theory. 
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I. I. Kinzina. Computation of the eigenvalues of a discrete selfadjoint operator perturbed by a bounded operator. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2008), pp. 16-24. http://geodesic.mathdoc.fr/item/IVM_2008_6_a1/

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