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

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


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




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

Diskr. Mat., 2010, Volume 22, Issue 1, Pages 17–49 (Mi dm1082)  
This article is cited in 2 scientific papers (total in 2 papers)

Fast algorithms for elementary operations on complex power series

I. S. Sergeev


Abstract: It is shown that the inversion of a complex-valued power series can be realised asymptotically with complexity of 5/4 multiplications (if we compare the upper bounds). It is shown that the calculation of the square root requires asymptotically also no more than 5/4 multiplications, the computation of an exponential has the complexity equal to 13/6 multiplications, and raising to an arbitrary power requires 41/12 multiplications.

DOI: https://doi.org/10.4213/dm1082

Full text: PDF file (287 kB)
References: PDF file   HTML file

English version:
Discrete Mathematics and Applications, 2010, 20:1, 25–60

Bibliographic databases:

UDC: 519.7
Received: 02.08.2008

Citation: I. S. Sergeev, “Fast algorithms for elementary operations on complex power series”, Diskr. Mat., 22:1 (2010), 17–49; Discrete Math. Appl., 20:1 (2010), 25–60

Citation in format AMSBIB
\Bibitem{Ser10}
\by I.~S.~Sergeev
\paper Fast algorithms for elementary operations on complex power series
\jour Diskr. Mat.
\yr 2010
\vol 22
\issue 1
\pages 17--49
\mathnet{http://mi.mathnet.ru/dm1082}
\crossref{https://doi.org/10.4213/dm1082}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2675429}
\zmath{https://zbmath.org/?q=an:05779531}
\elib{https://elibrary.ru/item.asp?id=20730322}
\transl
\jour Discrete Math. Appl.
\yr 2010
\vol 20
\issue 1
\pages 25--60
\crossref{https://doi.org/10.1515/DMA.2010.002}


Linking options:
  • http://mi.mathnet.ru/eng/dm1082
  • https://doi.org/10.4213/dm1082
  • http://mi.mathnet.ru/eng/dm/v22/i1/p17

    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. Yu. V. Kuznetsov, M. M. Petrunin, “Bystryi algoritm proverki vyrozhdennosti gankelevykh matrits”, Chebyshevskii sb., 12:2 (2011), 60–67  mathnet  mathscinet
    2. Bostan A., Jeannerod C.-P., Mouilleron C., Schost E., “On Matrices With Displacement Structure: Generalized Operators and Faster Algorithms”, SIAM J. Matrix Anal. Appl., 38:3 (2017), 733–775  crossref  mathscinet  zmath  isi  scopus
    		• Дискретная математика
    Number of views:
    This page:464
    Full text:179
    References:33
    First page:24
     
    Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021