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Zh. Vychisl. Mat. Mat. Fiz., 2013, Volume 53, Number 5, Pages 691–700 (Mi zvmmf9850)  

This article is cited in 1 scientific paper (total in 1 paper)

An extension of the Krylov method for calculating the coefficients of the minimal polynomial

K. O. Vidyaeva, S. M. Ermakov

Saint-Petersburg State University

Abstract: The concept of a $k$-minimal polynomial of an operator is introduced, and a method for approximate calculation of the coefficients of this polynomial is proposed. The method uses the calculated values of certain functionals on iterations of the operator. Special features emerging when the algorithm is used in combination with the Monte-Carlo method are discussed, and numerical results are given.

Key words: algorithm for calculating the coefficients of a polynomial, generalized Krylov method, Monte-Carlo method, spectrum of a linear operator.

DOI: https://doi.org/10.7868/S0044466913050153

Full text: PDF file (230 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2013, 53:5, 521–529

Bibliographic databases:

UDC: 519.61
Received: 15.06.2012
Revised: 28.11.2012

Citation: K. O. Vidyaeva, S. M. Ermakov, “An extension of the Krylov method for calculating the coefficients of the minimal polynomial”, Zh. Vychisl. Mat. Mat. Fiz., 53:5 (2013), 691–700; Comput. Math. Math. Phys., 53:5 (2013), 521–529

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Volf D.A., “Programmnaya realizatsiya podsistemy bystrogo singulyarnogo spektralnogo analiza rechi”, Sistemy upravleniya i informatsionnye tekhnologii, 54:4 (2013), 81–86  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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