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Faster relaxed multiplication

Abstract : In previous work, we have introduced several fast algorithms for relaxed power series multiplication (also known under the name on-line multiplication) up till a given order n. The fastest currently known algorithm works over an effective base field K with sufficiently many 2^p-th roots of unity and has algebraic time complexity O(n log n exp (2 sqrt (log 2 log log n))). In this note, we will generalize this algorithm to the cases when K is replaced by an effective ring of positive characteristic or by an effective ring of characteristic zero, which is also torsion-free as a Z-module and comes with an additional algorithm for partial division by integers. We will also present an asymptotically faster algorithm for relaxed multiplication of p-adic numbers.
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https://hal.archives-ouvertes.fr/hal-00687479
Contributor : Joris van der Hoeven Connect in order to contact the contributor
Submitted on : Tuesday, April 29, 2014 - 10:14:29 PM
Last modification on : Wednesday, November 18, 2020 - 10:32:03 PM
Long-term archiving on: : Tuesday, July 29, 2014 - 2:05:19 PM

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  • HAL Id : hal-00687479, version 2

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Joris van der Hoeven. Faster relaxed multiplication. 2012. ⟨hal-00687479v2⟩

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