Vestnik of Samara University. Natural Science SeriesVestnik of Samara University. Natural Science Series2541-75252712-8954Samara National Research University468010.18287/2541-7525-2013-19-9.1-5-11NUMERICAL METHOD FOR SOLVING INVERSE SPECTRAL PROBLEMS GENERATED BY PERTURBED SELF-ADJOINT OPERATORSKadchenkoS.I.morenov.sv@ssau.ruSouth-Ural State University01092013199.15110206201702062017Copyright © 2013, Kadchenko S.2013A new numerical method for solving inverse spectral problems generated by perturbed self-adjoint operators from their spectral characteristics is developed. The method was tested on the problems for perturbed Sturm - Liouville operator. The results of numerous calculations have shown its computational efficiency. The simple algebraic formulas for finding the eigenvalues of discrete operators was found. At that the calculation of eigenvalues of perturbed self-adjoint operator can start from any number, no matter known the eigenvalues from previous numbers or not.discrete operators, self-adjoint operators, eigenvalues, eigenfunctions, inverse spectral problems, Fredholm integral equation of the first kind, improperly posed problems, Sturm – Liouville problemдискретные операторы, самосопряженные операторы, соб- ственные значения, собственные функции, обратные спектральные задачи, инте- гральное уравнение Фредгольма первого рода, некорректно поставленные задачи, задача Штурма — Лиувилля