WSEAS Transactions on Systems and Control


Print ISSN: 1991-8763
E-ISSN: 2224-2856

Volume 14, 2019

Notice: As of 2014 and for the forthcoming years, the publication frequency/periodicity of WSEAS Journals is adapted to the 'continuously updated' model. What this means is that instead of being separated into issues, new papers will be added on a continuous basis, allowing a more regular flow and shorter publication times. The papers will appear in reverse order, therefore the most recent one will be on top.


Volume 14, 2019



The Interpolation Method for Calculating Eigenvalues of Matrices

AUTHORS: I. G. Burova, V. M. Ryabov, M. A. Kalnitskaia, A. V. Malevich

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ABSTRACT: The problem of solving systems of linear algebraic equations (SLAEs) is connected with finding the eigenvalues of the matrix of the system. Often it is necessary to solve SLAEs with positive definite symmetric matrices. The eigenvalues of such matrices are real and positive. Here we propose an interpolation method for finding eigenvalues of such matrices. The proposed method can also be used to calculate the real eigenvalues of an arbitrary matrix with real elements. This method uses splines of Lagrangian type of fifth order and/or polynomial integro-differential splines of fifth order. To calculate the eigenvalue, it is necessary to calculate several determinants and solve the nonlinear equation. Examples of numerical experiments are given.

KEYWORDS: - eigenvalue problem, integro-differential splines, approximation

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[4] Rezgui H., Choutri A., An inverse eigenvalue problem. Application: Graded-index optical fibers, Optical and Quantum Electronics, October 2017, pp. 49-321.

[5] Burova Irina, On Integro-Differential Splines Construction. In: Advances in Applied and Pure Mathematics, Proceedings of the 7th International Conference on Finite Differences, Finite Elements, Finite Volumes, Boundary Elements (F-and-B’14), Gdansk, Poland, May 15-17, 2014, pp. 57-61.

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[8] Dem'yanovich Yu.K., Approximation by Minimal Splines. J. of Math. Sci., Vol.193, No 2, 2013, pp. 261-266.

[9] Burova I.G., Construction of trigonometric splines, Vestnik St. Petersburg University: Mathematics, Vol. 37, No 2, 2004, pp. 6-11.

[10] de Boor Carl, A Practical Guide to Splines, Springer-Verlag. New York. Heidelberg Berlin, 1978.

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WSEAS Transactions on Systems and Control, ISSN / E-ISSN: 1991-8763 / 2224-2856, Volume 14, 2019, Art. #13, pp. 104-111


Copyright Β© 2019 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution License 4.0

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