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

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...

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Published inJournal of mathematical sciences (New York, N.Y.) Vol. 241; no. 5; pp. 570 - 588
Main Authors Kadchenko, S. I., Kakushkin, S. N.
Format Journal Article
LanguageEnglish
Published New York Springer US 04.09.2019
Springer
Springer Nature B.V
Subjects
Algorithms
Eigenvalues
Eigenvectors
Mathematical analysis
Mathematics
Mathematics and Statistics
Numerical methods
Operators
Spectra
self-adjoint operator
47J10
numerical methods
65L15
method of regularized traces
spectrum
34L05
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ISSN1072-3374
1573-8795
DOI10.1007/s10958-019-04446-z

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Summary: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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ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-019-04446-z