This article is cited in 3 scientific papers (total in 3 papers)
Remarks on the fast multiplication of polynomials, and Fourier and Hartley transforms
S. B. Gashkov
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.
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Discrete Mathematics and Applications, 2000, 10:5, 499–528
S. B. Gashkov, “Remarks on the fast multiplication of polynomials, and Fourier and Hartley transforms”, Diskr. Mat., 12:3 (2000), 124–153; Discrete Math. Appl., 10:5 (2000), 499–528
Citation in format AMSBIB
\paper Remarks on the fast multiplication of polynomials, and Fourier and Hartley transforms
\jour Diskr. Mat.
\jour Discrete Math. Appl.
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This publication is cited in the following articles:
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
S. B. Gashkov, I. S. Sergeev, “Slozhnost vychislenii v konechnykh polyakh”, Fundament. i prikl. matem., 17:4 (2012), 95–131 ; S. B. Gashkov, I. S. Sergeev, “Complexity of computation in finite fields”, J. Math. Sci., 191:5 (2013), 661–685
Burtsev A.A., Gashkov S.B., “O skhemakh dlya arifmetiki v konechnykh polyakh”, Trudy moskovskogo fiziko-tekhnicheskogo instituta, 2012, 15–22
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