Geodesic
The Algorithm of Finding of Meanings of Eigenfunctions of Perturbed Self-Adjoin Operators Via Method of Regularized Traces
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, no. 14 (2012), pp. 83-88

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The article is a continuation of the work, which accordance with development numerical noniterations method, allowing to find meanings of first eigenfunctions perturbed self-adjoin operators in the nodes of the sampling. Difficulty of the using method RT without direct decision of the systems of the nonlinear equations connected with expression of meanings of eigenfunctions of perturbed discrete operators from product the eigenfunction of the perturbed operator on its associate. In this work is offered computing efficient algorithm, allowing avoid this difficulty. The designed methods was checked on example of the spectral problem of the finding of meanings of eigenfunctions of perturbed Laplas's operator. From result of the calculation is seen that found meanings of eigenfunctions well agree with result, got by well-known methods by A. N. Krylov and A. M. Danilevskiy.
Keywords: eigenvalues, eigenfunctions, «weighted» corrections of the perturbation theory, self-adjoin operators. 
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     author = {S. I. Kadchenko and S. N. Kakushkin},
     title = {The {Algorithm} of {Finding} of {Meanings} of {Eigenfunctions} of {Perturbed} {Self-Adjoin} {Operators} {Via} {Method} of {Regularized} {Traces}},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
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S. I. Kadchenko; S. N. Kakushkin. The Algorithm of Finding of Meanings of Eigenfunctions of Perturbed Self-Adjoin Operators Via Method of Regularized Traces. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, no. 14 (2012), pp. 83-88. http://geodesic.mathdoc.fr/item/VYURU_2012_14_a7/