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Journal Articles Applicable Algebra in Engineering, Communication and Computing Year : 2004

The Middle Product Algorithm I. Speeding up the division and square root of power series

Abstract

We present new algorithms for the inverse, division, and square root of power series. The key trick is a new algorithm --- {\tt MiddleProduct} or, for short, {\tt MP} --- computing the $n$ middle coefficients of a $(2n-1) \times n$ full product in the same number of multiplications as a full $n \times n$ product. This improves previous work of Brent, Mulders, Karp and Markstein, Burnikel and Ziegler. These results apply both to series and polynomials.
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Dates and versions

inria-00100147 , version 1 (26-09-2006)

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  • HAL Id : inria-00100147 , version 1

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Guillaume Hanrot, Michel Quercia, Paul Zimmermann. The Middle Product Algorithm I. Speeding up the division and square root of power series. Applicable Algebra in Engineering, Communication and Computing, 2004, 14 (6), pp.415-438. ⟨inria-00100147⟩
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