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Calculation of Spectral Characteristics of Perturbed Self-Adjoint Operators by Methods of Regularized Traces

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Abstract

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

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  1. G. I. Nosov Magnitogorsk State Technical University, Magnitogorsk, Russia

    S. I. Kadchenko & S. N. Kakushkin

  2. Institute of Natural Sciences of the South-Ural State University, Chelyabinsk, Russia

    S. I. Kadchenko

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  1. S. I. Kadchenko
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Correspondence to S. I. Kadchenko.

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 141, Differential Equations. Spectral Theory, 2017.

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Kadchenko, S.I., Kakushkin, S.N. Calculation of Spectral Characteristics of Perturbed Self-Adjoint Operators by Methods of Regularized Traces. J Math Sci 241, 570–588 (2019). https://doi.org/10.1007/s10958-019-04446-z

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