# Speeding up the inversion of power series

1 POLKA - Polynomials, Combinatorics, Arithmetic
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : We present a new algorithm to compute the $n$ middle coefficients of a $2n \times n$ product in $K(n)$ ring operations, where $K(n)$ is the number of operations needed by Karatsuba's algorithm for a full $n \times n$ product. Used in Newton iteration, and together with previous work of Mulders, Karp and Markstein, this algorithm enables one to compute an inverse in $\sim 0.904 \, K(n)$ operations, a quotient in $\sim 1.173 \, K(n)$ operations, and a square root in $\sim 0.891 \, K(n)$ operations. These results apply both to power series and polynomials.
Mots-clés :
Type de document :
Rapport
[Intern report] A00-R-067 || hanrot00a, 2000, 8 p
Domaine :

https://hal.inria.fr/inria-00099294
Contributeur : Publications Loria <>
Soumis le : mardi 26 septembre 2006 - 08:52:33
Dernière modification le : jeudi 11 janvier 2018 - 06:19:48

### Identifiants

• HAL Id : inria-00099294, version 1

### Citation

Guillaume Hanrot, Paul Zimmermann. Speeding up the inversion of power series. [Intern report] A00-R-067 || hanrot00a, 2000, 8 p. 〈inria-00099294〉

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