The Middle Product Algorithm I

Authors:
Guillaume Hanrot;Michel Quercia;Paul Zimmermann
Affiliations:
INRIA-Lorraine/LORIA, France;INRIA-Lorraine/LORIA, France;INRIA-Lorraine/LORIA, France
Venue:
Applicable Algebra in Engineering, Communication and Computing
Year:
2004

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Abstract

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