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

Article Dans Une Revue Applicable Algebra in Engineering, Communication and Computing Année : 2004

Résumé

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 nnn middle coefficients of a (2n−1)timesn(2n-1) \times n(2n−1)timesn full product in the same number of multiplications as a full ntimesnn \times nntimesn product. This improves previous work of Brent, Mulders, Karp and Markstein, Burnikel and Ziegler. These results apply both to series and polynomials.

Mots clés

• middle product
• inversion
• division
• square root
• inverse
• racine carrée
• méthode de newton
• newton's method
• produit médian

Dates et versions

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

Identifiants

• HAL Id : inria-00100147 , version 1

Citer

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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