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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

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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}


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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. 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
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