S. I. Kadchenko, S. N. Kakushkin, “Calculation of spectral characteristics of perturbed self-adjoint operators by methods of regularized traces”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 2017, Volume 141,Pages <nobr>61

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Calculation of spectral characteristics of perturbed self-adjoint operators by methods of regularized traces

S. I. Kadchenko^ab, S. N. Kakushkin^a

^a Magnitogorsk State Technical University
^b South Ural State University, Chelyabinsk

Abstract: We discuss basic theoretical principles underlying new numerical methods of calculation of eigenvalues and eigenfunctions of discrete, semi-bounded from below operators. We present algorithms of finding spectral characteristics by methods of regularized traces and examples related to certain spectral Sturm–Liouville problems.

Keywords: self-adjoint operator, method of regularized traces, numerical methods, spectrum.

UDC: 517.984.22, 519.614

MSC: 34L05, 47J10, 65L15