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 Diskr. Mat., 2011, Volume 23, Issue 1, Pages 28–45 (Mi dm1128)

Calculation of the characteristic polynomial of a matrix

O. N. Pereslavtseva

Abstract: We consider efficient algorithms of calculation of the characteristic polynomials of matrices over commutative rings. We give estimates of complexity treated as the number of ring operations, and for the ring of integers the estimates are presented in terms of the number of multiplication operations over the machine words. We suggest a new algorithm to calculate the characteristic polynomial which has the best estimate of complexity in the ring operations. We give recommendations concerning applications of the algorithm of calculation of the characteristic polynomials depending on the size of the matrix, in particular, the algorithm suggested in this paper is recommended to be applied to integer-element matrices of size greater than 60.

DOI: https://doi.org/10.4213/dm1128

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English version:
Discrete Mathematics and Applications, 2011, 21:1, 109–129

Bibliographic databases:

UDC: 519.7
Revised: 29.01.2011

Citation: O. N. Pereslavtseva, “Calculation of the characteristic polynomial of a matrix”, Diskr. Mat., 23:1 (2011), 28–45; Discrete Math. Appl., 21:1 (2011), 109–129

Citation in format AMSBIB
\Bibitem{Per11} \by O.~N.~Pereslavtseva \paper Calculation of the characteristic polynomial of a~matrix \jour Diskr. Mat. \yr 2011 \vol 23 \issue 1 \pages 28--45 \mathnet{http://mi.mathnet.ru/dm1128} \crossref{https://doi.org/10.4213/dm1128} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2830695} \elib{http://elibrary.ru/item.asp?id=20730370} \transl \jour Discrete Math. Appl. \yr 2011 \vol 21 \issue 1 \pages 109--129 \crossref{https://doi.org/10.1515/DMA.2011.008} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79953309752} 

• http://mi.mathnet.ru/eng/dm1128
• https://doi.org/10.4213/dm1128
• http://mi.mathnet.ru/eng/dm/v23/i1/p28

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This publication is cited in the following articles:
1. Pereslavtseva O.N., “Parallelnyi modulyarnyi algoritm vychisleniya kharakteristicheskogo polinoma matritsy v koltse polinomov mnogikh peremennykh”, Vestn. Tambovskogo un-ta. Ser. Estestvennye i tekhnicheskie nauki, 17:2 (2012), 588–590
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