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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2013, Volume 53, Number 5, Pages 691–700
DOI: https://doi.org/10.7868/S0044466913050153 (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
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DOI: https://doi.org/10.7868/S0044466913050153
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.
Received: 15.06.2012
Revised: 28.11.2012
English version:
Computational Mathematics and Mathematical Physics, 2013, Volume 53, Issue 5, Pages 521–529
DOI: https://doi.org/10.1134/S0965542513050138
Bibliographic databases:
Document Type: Article
UDC: 519.61
Language: Russian
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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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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