Geodesic
Generalization of method A. A. Dorodnicyn close calculation of eigenvalues and eigenvectors of symmetric matrices on case of self-conjugate discrete operators
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 11 (2011) no. 3, pp. 20-29 
E. M. Maleko. Generalization of method A. A. Dorodnicyn close calculation of eigenvalues and eigenvectors of symmetric matrices on case of self-conjugate discrete operators. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 11 (2011) no. 3, pp. 20-29. http://geodesic.mathdoc.fr/item/ISU_2011_11_3_a3/
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Let the discrete self-conjugate operator $A$ operates in separable Hilbert space $\mathbb H$ and has the kernel resolvent with simple spectrum. Self-conjugate and limited operator $B$ operates also in $\mathbb H$. Then it is possible to find such number $\varepsilon>0$, that eigenvalues and eigenfunctions of the perturbation operator $A+\varepsilon B$ will be calculated on a method of Dorodnicyn.

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