Standard

The interpolation method for calculating eigenvalues of matrices. / Burova, I. G.; Ryabov, V. M.; Kalnitskaia, M. A.; Malevich, A. V.

In: WSEAS Transactions on Systems and Control, Vol. 14, 13, 01.01.2019, p. 104-111.

Research output: Contribution to journal › Article › peer-review

Harvard

Burova, IG, Ryabov, VM, Kalnitskaia, MA & Malevich, AV 2019, 'The interpolation method for calculating eigenvalues of matrices', WSEAS Transactions on Systems and Control, vol. 14, 13, pp. 104-111.

APA

Burova, I. G., Ryabov, V. M., Kalnitskaia, M. A., & Malevich, A. V. (2019). The interpolation method for calculating eigenvalues of matrices. WSEAS Transactions on Systems and Control, 14, 104-111. [13].

Vancouver

Burova IG, Ryabov VM, Kalnitskaia MA, Malevich AV. The interpolation method for calculating eigenvalues of matrices. WSEAS Transactions on Systems and Control. 2019 Jan 1;14:104-111. 13.

Author

Burova, I. G. ; Ryabov, V. M. ; Kalnitskaia, M. A. ; Malevich, A. V. / The interpolation method for calculating eigenvalues of matrices. In: WSEAS Transactions on Systems and Control. 2019 ; Vol. 14. pp. 104-111.

BibTeX

@article{4c0f7e49a23a40828143fc06c4079c14,
title = "The interpolation method for calculating eigenvalues of matrices",
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 = "Approximation, Eigenvalue problem, Integro-differential splines",
author = "Burova, {I. G.} and Ryabov, {V. M.} and Kalnitskaia, {M. A.} and Malevich, {A. V.}",
year = "2019",
month = jan,
day = "1",
language = "English",
volume = "14",
pages = "104--111",
journal = "WSEAS Transaction on Systems and Control",
issn = "1991-8763",
publisher = "WORLD SCIENTIFIC PUBL CO PTE LTD",

}

RIS

TY - JOUR

T1 - The interpolation method for calculating eigenvalues of matrices

AU - Burova, I. G.

AU - Ryabov, V. M.

AU - Kalnitskaia, M. A.

AU - Malevich, A. V.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - Approximation

KW - Eigenvalue problem

KW - Integro-differential splines

UR - http://www.scopus.com/inward/record.url?scp=85071012928&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85071012928

VL - 14

SP - 104

EP - 111

JO - WSEAS Transaction on Systems and Control

JF - WSEAS Transaction on Systems and Control

SN - 1991-8763

M1 - 13

ER -

ID: 45515149