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Mat. Zametki, 2013, Volume 94, Issue 2, Pages 175–182 (Mi mz9345)  

This article is cited in 6 scientific papers (total in 6 papers)

On the Calculation of Functions of Matrices

Yu. N. Belyaev

Syktyvkar State University

Abstract: The representation of entire functions of matrices via symmetric polynomials of $n$th 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 $n$th order, matrix exponential, numerical calculation of functions of matrices.

DOI: https://doi.org/10.4213/mzm9345

Full text: PDF file (416 kB)
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English version:
Mathematical Notes, 2013, 94:2, 177–184

Bibliographic databases:

UDC: 512.64
Received: 03.03.2012
Revised: 30.09.2012

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

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Yu. N. Belyayev, “Characteristic matrices of layered periodic structures”, Proceedings of the International Conference Days on Diffraction 2015, IEEE, 2015, 42–48  isi
    2. 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
    3. 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
    4. 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  isi
    5. 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
    6. 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
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