FINDING EIGENFUNCTIONS OF PERTURBED SELF-ADJOINT OPERATORS GIVEN ON A COMPACT GRAPH

Abstract

The substantiation of a numerical method for finding the eigenfunctions of perturbed self-adjoint operators given in a separable Hilbert space is considered. The method is adapted for problems given on finite connected oriented graphs with an arbitrary number of edges and vertices. The non-iterative numerical method is based on simple formulas using information about the spectral charac-teristics of an unperturbed operator and its perturbing operator. Approximation of the perturbed operator by a matrix is not required. As an example, the developed technique is applied to a perturbed spectral problem given on a three-edge graph of the "star" type. The results of a computational experiment conducted using a software package written in the Maple mathematical environment are presented.