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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
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\paper Fast algorithms for elementary operations on complex power series
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\issue 1
\pages 17--49
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\crossref{https://doi.org/10.4213/dm1082}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2675429}
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\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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http://mi.mathnet.ru/eng/dm1082https://doi.org/10.4213/dm1082 http://mi.mathnet.ru/eng/dm/v22/i1/p17
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Yu. V. Kuznetsov, M. M. Petrunin, “Bystryi algoritm proverki vyrozhdennosti gankelevykh matrits”, Chebyshevskii sb., 12:2 (2011), 60–67
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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
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