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Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya, 2013, Issue 9/1(110), Pages 5–11 (Mi vsgu393)  

This article is cited in 2 scientific papers (total in 3 papers)

Mathematics

Numerical method for solving inverse spectral problems generated by perturbed self-adjoint operators

S. I. Kadchenko

Dept. of Mathematical Physics Equations, South-Ural State University, Chelyabinsk, 454080, Russian Federation

Abstract: A 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.

Keywords: discrete operators, self-adjoint operators, eigenvalues, eigenfunctions, inverse spectral problems, Fredholm integral equation of the first kind, improperly posed problems, Sturm–Liouville problem.

Full text: PDF file (132 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
References: PDF file   HTML file
UDC: 519.6
Received: 15.09.2013

Citation: S. I. Kadchenko, “Numerical method for solving inverse spectral problems generated by perturbed self-adjoint operators”, Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya, 2013, no. 9/1(110), 5–11

Citation in format AMSBIB
\Bibitem{Kad13}
\by S.~I.~Kadchenko
\paper Numerical method for solving inverse spectral problems generated by~perturbed self-adjoint operators
\jour Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya
\yr 2013
\issue 9/1(110)
\pages 5--11
\mathnet{http://mi.mathnet.ru/vsgu393}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. I. Kadchenko, G. A. Zakirova, “A numerical method for inverse spectral problems”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 8:3 (2015), 116–126  mathnet  crossref  elib
    2. G. A. Zakirova, E. V. Kirillov, “The existence of solution of the inverse spectral problem for discrete self-adjoint semi-bounded from below operator”, J. Comp. Eng. Math., 2:4 (2015), 95–99  mathnet  crossref  elib
    3. A. V. Keller, G. A. Sviridyuk, S. A. Zagrebina, G. A. Zakirova, E. V. Bychkov, P. O. Moskvicheva, O. Tsyplenkova, “Sergei Ivanovich Kadchenko (to the 65th anniversary)”, J. Comp. Eng. Math., 2:4 (2015), 100–102  mathnet  elib
  • Вестник Самарского государственного университета. Естественнонаучная серия
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