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Matematicheskie Zametki, 2013, Volume 94, Issue 2, Pages 175–182
DOI: https://doi.org/10.4213/mzm9345 (Mi mzm9345) 		 
This article is cited in 12 scientific papers (total in 12 papers)

On the Calculation of Functions of Matrices

Yu. N. Belyaev

Syktyvkar State University
Full-text PDF (416 kB) Citations (12)
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DOI: https://doi.org/10.4213/mzm9345
Abstract: The representation of entire functions of matrices via symmetric polynomials of nnth order is obtained. A method of deriving analytic formulas for functions of matrices of second, third, and fourth orders is obtained. Symmetric polynomials are used to construct algorithms for the numerical calculations of entire functions of matrices, in particular, of matrix exponentials, not requiring the determination of the eigenvalues of the matrices. The efficiency of the proposed numerical methods is estimated.
Keywords: entire function of a matrix, symmetric polynomial of nnth order, matrix exponential, numerical calculation of functions of matrices.
Received: 03.03.2012
Revised: 30.09.2012
English version:
Mathematical Notes, 2013, Volume 94, Issue 2, Pages 177–184
DOI: https://doi.org/10.1134/S0001434613070171
Bibliographic databases:
Document Type: Article
UDC: 512.64
Language: Russian
Citation: Yu. N. Belyaev, “On the Calculation of Functions of Matrices”, Mat. Zametki, 94:2 (2013), 175–182; Math. Notes, 94:2 (2013), 177–184
Citation in format AMSBIB
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    • This publication is cited in the following 12 articles:
    1. Ernesto Estrada, “The many facets of the Estrada indices of graphs and networks”, SeMA, 79:1 (2022), 57  crossref
    2. Belyayev Yu.N., “Method For Calculating Multiwave Scattering By Layered Anisotropic Media”, Wave Motion, 99 (2020), 102664  crossref  mathscinet  isi  scopus
    3. Yu. N. Belyayev, “Calculation of the six-beam diffraction in layered media using polynomials of principal minors”, J. Theor. Comput. Acoust., 26:2 (2018), UNSP 1850017, 21 pp.  crossref  mathscinet  isi  scopus
    4. Yu. N. Belyayev, “The method of polynomials of principal minors in calculations of acoustic stresses in an anisotropic layer”, Mechanics, Resource and Diagnostics of Materials and Structures (MRDMS-2018), AIP Conf. Proc., 2053, eds. E. Gorkunov, V. Panin, S. Ramasubbu, Amer. Inst. Phys., 2018, UNSP 040008  crossref  isi  scopus
    5. Yu N Belyayev, “Analytical solutions for multi-wave transfer matrices in layered structures”, J. Phys.: Conf. Ser., 1092 (2018), 012008  crossref
    6. Yu. N. Belyayev, “Conversion of elastic waves as a result of diffraction in anisotropic layer”, Winter School on Continuous Media Mechanics, IOP Conference Series-Materials Science and Engineering, 208, IOP Publishing Ltd, 2017, UNSP 012003  crossref  isi  scopus
    7. Belyayev Yu.N., “On the Calculation of Matrix Exponential of a Large Order”, Proceedings of the International Conference Days on Diffraction (Dd) 2017, eds. Motygin O., Kiselev A., Goray L., Suslina T., Kazakov A., Kirpichnikova A., IEEE, 2017, 55–59  crossref  isi
    8. Yu. N. Belyayev, “Characteristic matrices of layered periodic structures”, Proceedings of the International Conference Days on Diffraction 2015, IEEE, 2015, 42–48  isi
    9. Yu. N. Belyayev, S. O. Gridnev, A. M. Dronov, “Coefficients of SH-wave conversion into SV- and P-waves by the crystal layer”, Proceedings of the International Conference Days on Diffraction 2015, IEEE, 2015, 49–53  isi
    10. Yuriy N. Belyayev, 2015 Days on Diffraction (DD), 2015, 1  crossref
    11. Yuriy N. Belyayev, Sergey O. Gridnev, Alexander M. Dronov, 2015 Days on Diffraction (DD), 2015, 1  crossref
    12. Yuriy N. Belyayev, Proceedings of the International Conference Days on Diffraction 2014, 2014, 37  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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