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Diskretnaya Matematika, 2010, Volume 22, Issue 1, Pages 17–49
DOI: https://doi.org/10.4213/dm1082 (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
Full-text PDF (287 kB) Citations (2)
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DOI: https://doi.org/10.4213/dm1082
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.
Received: 02.08.2008
English version:
Discrete Mathematics and Applications, 2010, Volume 20, Issue 1, Pages 25–60
DOI: https://doi.org/10.1515/DMA.2010.002
Bibliographic databases:
Document Type: Article
UDC: 519.7
Language: Russian
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://mathscinet.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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  • https://doi.org/10.4213/dm1082
  • https://www.mathnet.ru/eng/dm/v22/i1/p17
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Дискретная математика
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    Full-text PDF :262
    References:57
    First page:24
     
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