Prikladnaya Diskretnaya Matematika
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Prikl. Diskr. Mat.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Prikl. Diskr. Mat., 2011, Number 4(14), Pages 72–88 (Mi pdm347)  

This article is cited in 2 scientific papers (total in 2 papers)

Computational Methods in Discrete Mathematics

Regular estimates for the complexity of polynomial multiplication and truncated Fourier transform

I. S. Sergeev

M. V. Lomonosov Moscow State University, Moscow, Russia

Abstract: In the present paper, some polynomial multiplication circuits being efficient either in complexity and depth or in complexity and memory size are proposed. Consequently, for instance, the multiplication of polynomials of the sum degree $n-1$, where $n=2^{n_1}+…+2^{n_s}$, $n_1>…>n_s$, over a ring with invertible 2 can be implemented via $M(n_1)+…+M(n_s)+\mathrm O(n)$ arithmetic operations over the ring with the depth $\max_i\{D(n_i)\}+\mathrm O(\log n)$, where $M(k)$ and $D(k)$ are respectively the complexity and the depth of the modulo $x^{2^k}+1$ multiplication circuit. As another example, the truncated DFT of order $n$ (i.e. the DFT of order $2^{\lceil\log_2n\rceil}$ reduced to the vectors of dimension $n$) can be implemented by a circuit of complexity $1,5n\log_2n+\mathrm O(n)$ and memory size $n+1$.

Keywords: arithmetic circuits, complexity, depth, memory size, multiplication, Discrete Fourier Transform.

Full text: PDF file (669 kB)
References: PDF file   HTML file
UDC: 519.7

Citation: I. S. Sergeev, “Regular estimates for the complexity of polynomial multiplication and truncated Fourier transform”, Prikl. Diskr. Mat., 2011, no. 4(14), 72–88

Citation in format AMSBIB
\Bibitem{Ser11}
\by I.~S.~Sergeev
\paper Regular estimates for the complexity of polynomial multiplication and truncated Fourier transform
\jour Prikl. Diskr. Mat.
\yr 2011
\issue 4(14)
\pages 72--88
\mathnet{http://mi.mathnet.ru/pdm347}


Linking options:
  • http://mi.mathnet.ru/eng/pdm347
  • http://mi.mathnet.ru/eng/pdm/y2011/i4/p72

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. Veretekhina S.V., Zhuravlyov M.S., Shmakova E.G., Soldatov A.A., Kotenev A.V., Kashirin S.V., Medvedeva A.V., “Analog Sound Signals Digitalization and Processing”, Mod. J. Lang. Teach. Methods, 8:3 (2018), 45–63  isi
    2. S. B. Gashkov, I. S. Sergeev, “Umnozhenie”, Chebyshevskii sb., 21:1 (2020), 101–134  mathnet  crossref
  • Прикладная дискретная математика
    Number of views:
    This page:204
    Full text:62
    References:25

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2022