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The Middle Product Algorithm, I.

Guillaume Hanrot 1 Michel Quercia Paul Zimmermann 1
1 SPACES - Solving problems through algebraic computation and efficient software
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
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. A forthcoming paper will study the floating-point case.
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https://hal.inria.fr/inria-00071921
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Submitted on : Tuesday, May 23, 2006 - 7:16:27 PM
Last modification on : Friday, February 4, 2022 - 3:30:42 AM
Long-term archiving on: : Sunday, April 4, 2010 - 10:44:37 PM

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  • HAL Id : inria-00071921, version 1

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Guillaume Hanrot, Michel Quercia, Paul Zimmermann. The Middle Product Algorithm, I.. [Research Report] RR-4664, INRIA. 2002. ⟨inria-00071921⟩

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