# Speeding up the Division and Square Root of Power Series

1 POLKA - Polynomials, Combinatorics, Arithmetic
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : We present new algorithms for the inverse, quotient, or square root of power series. The key trick is a new algorithm -- RecursiveMiddleProduct or RMP -- computing the $n$ middle coefficients of a $2n x n$ product in essentially the same number of operations -- $K(n)$ -- than a full $n x n$ product with Karatsuba's method. This improves previous work of Mulders, Karp and Markstein, Burnikel and Ziegler. These results apply both to series, polynomials, and multiple precision floating-point numbers.
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https://hal.inria.fr/inria-00072675
Contributor : Rapport de Recherche Inria <>
Submitted on : Wednesday, May 24, 2006 - 10:33:36 AM
Last modification on : Friday, February 26, 2021 - 3:28:02 PM
Long-term archiving on: : Sunday, April 4, 2010 - 11:17:52 PM

### Identifiers

• HAL Id : inria-00072675, version 1

### Citation

Guillaume Hanrot, Michel Quercia, Paul Zimmermann. Speeding up the Division and Square Root of Power Series. [Research Report] RR-3973, INRIA. 2000, pp.20. ⟨inria-00072675⟩

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