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

Guillaume Hanrot 1 Michel Quercia Paul Zimmermann 1
1 SPACES - Solving problems through algebraic computation and efficient software
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
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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Submitted on : Tuesday, September 26, 2006 - 10:14:39 AM
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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, Springer Verlag, 2004, 14 (6), pp.415-438. ⟨inria-00100147⟩

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