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J. Comp. Eng. Math., 2017, Volume 4, Issue 1, Pages 38–47 (Mi jcem82)  

Computational Mathematics

Calculation of eigenvalues of discrete semibounded differential operators

S. I. Kadchenkoa, G. A. Zakirovab

a Nosov Magnitogorsk State Technical University (Magnitogorsk, Russian Federation)
b South Ural State University (Chelyabinsk, Russian Federation)

Abstract: We consider a problem of eigenvalues of an abstract discrete semibounded operator acting in a separable Hilbert space. The existence and uniqueness of the solution, as well as a convergence of the Galerkin method with reference to the problem, are proved. Simple formulas to calculate the eigenvalues are obtained. The formulas based on Galerkin method allow to calculate eigenvalues of discrete semibounded operators with high computational efficiency. In contrast to the classical methods, the formulas sharply reduce the number of calculations. Also, the formulas allow to find eigenvalues of the operator, regardless of whether the eigenvalues with smaller numbers are known or not. The formulas solve the problem on a calculation of all necessary spectrum points of the abstract discrete semibounded operators.

Keywords: eigenvalues, eigenfunctions, perturbation, discrete operator, Galerkin method, existence and uniqueness of the solution.

DOI: https://doi.org/10.14529/jcem170104

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Bibliographic databases:

UDC: 517.9
MSC: 47A55, 47A75
Received: 10.03.2017
Language:

Citation: S. I. Kadchenko, G. A. Zakirova, “Calculation of eigenvalues of discrete semibounded differential operators”, J. Comp. Eng. Math., 4:1 (2017), 38–47

Citation in format AMSBIB
\Bibitem{KadZak17}
\by S.~I.~Kadchenko, G.~A.~Zakirova
\paper Calculation of eigenvalues of discrete semibounded differential operators
\jour J. Comp. Eng. Math.
\yr 2017
\vol 4
\issue 1
\pages 38--47
\mathnet{http://mi.mathnet.ru/jcem82}
\crossref{https://doi.org/10.14529/jcem170104}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3637687}
\elib{http://elibrary.ru/item.asp?id=28921544}


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