I. G. Burova, V. M. Ryabov, M. A. Kalnitskaia, A. V. Malevich, "The Interpolation Method for Calculating Eigenvalues of Matrices," WSEAS Transactions on Systems and Control, vol. 14, pp. 104-111, 2019, DOI:
I. G. Burova, V. M. Ryabov, M. A. Kalnitskaia, A. V. Malevich. The Interpolation Method for Calculating Eigenvalues of Matrices.
WSEAS Transactions on Systems and Control. 2019;14:104-111.
WSEAS Transactions on Systems and Control
Print ISSN: 1991-8763, E-ISSN: 2224-2856
Volume 14, 2019
The Interpolation Method for Calculating Eigenvalues of Matrices
Authors: , , ,
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.
Pages: 104-111 WSEAS Transactions on Systems and Control, ISSN / E-ISSN: 1991-8763 / 2224-2856, Volume 14, 2019, Art. #13 DOI: *As the DOI is a unique identifier, it is already available in the pdf version.
**The DOI link will be activated in the first midst of January 2026.
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