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Diskr. Mat., 2000, Volume 12, Issue 3, Pages 124–153 (Mi dm340)  

This article is cited in 3 scientific papers (total in 3 papers)


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Remarks on the fast multiplication of polynomials, and Fourier and Hartley transforms

S. B. Gashkov


Abstract: We give a fast algorithm for multiplication of polynomials with real-valued coefficients without resort to complex numbers and the fast Fourier transformation. The efficiency of this algorithm is compared with the multiplication algorithm based on the discrete Hartley transformation. We demonstrate that the complexity of the Hartley transformation coincides, to within a linear term, with the complexity of the Fourier transformation, but the use of the Hartley transformation leads to a more efficient multiplication algorithm.
We give analogues of these results for finite fields. In some cases, the multiplicative constants in bounds for the complexity of multiplication of polynomials and of the Fourier and Hartley transformations over finite fields are smaller than those in the case of the field of real numbers.
This research was supported by the Russian Foundation for Basic Research, grant 99–01–01175, and the Federal Special Program ‘Integration’, grant 473.

UDC: 519.7

Received: 22.12.1999

Citation: S. B. Gashkov, “Remarks on the fast multiplication of polynomials, and Fourier and Hartley transforms”, Diskr. Mat., 12:3 (2000), 124–153

Citation in format AMSBIB
\Bibitem{Gas00}
\by S.~B.~Gashkov
\paper Remarks on the fast multiplication of polynomials, and Fourier and Hartley transforms
\jour Diskr. Mat.
\yr 2000
\vol 12
\issue 3
\pages 124--153
\mathnet{http://mi.mathnet.ru/dm340}
\crossref{http://dx.doi.org/10.4213/dm340}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1810959}
\zmath{http://zbmath.org/?q=an:1001.11060}
\transl
\jour Discrete Math. Appl.
\yr 2000
\vol 10
\issue 5
\pages 499--528


DOI: 10.4213/dm340

Linking options:
  • http://mi.mathnet.ru/eng/dm340
  • http://dx.doi.org/10.4213/dm340
  • http://mi.mathnet.ru/eng/dm/v12/i3/p124

    Full text (in Russian): PDF file (2522 kB)
    References (in Russian): PDF file   HTML файл

    English version:
    Discrete Mathematics and Applications, 2000, 10:5, 499–528

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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. Gashkov S.B., Gashkov I.B., “Some Remarks on Testing Irreducibility of Polynomials and Normality of Bases in Finite Fields”, Fundamenta Informaticae, 104:3 (2010), 227–238  mathscinet  zmath
    2. С. Б. Гашков, И. С. Сергеев, “Сложность вычислений в конечных полях”, Фундамент. и прикл. матем., 17:4 (2012), 95–131  mathnet; S. B. Gashkov, I. S. Sergeev, “Complexity of computation in finite fields”, J. Math. Sci., 191:5 (2013), 661–685  crossref
    3. Бурцев А.А., Гашков С.Б., “О схемах для арифметики в конечных полях”, Труды московского физико-технического института, 2012, 15–22  elib
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