Speeding up the Division and Square Root of Power Series - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Reports (Research Report) Year : 2000

Speeding up the Division and Square Root of Power Series

Guillaume Hanrot
  • Function : Author
  • PersonId : 831392
Michel Quercia
  • Function : Author

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.

Domains

Other [cs.OH]
Fichier principal
Vignette du fichier
RR-3973.pdf (332.55 Ko) Télécharger le fichier

Dates and versions

inria-00072675 , version 1 (24-05-2006)

Identifiers

  • HAL Id : inria-00072675 , version 1

Cite

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⟩
298 View
726 Download

Share

Gmail Mastodon Facebook X LinkedIn More