NDLI: Faster relaxed multiplication

Content Provider	ACM Digital Library
Author	van der Hoeven, Joris
Abstract	In previous work, we have introduced several fast algorithms for relaxed power series multiplication (also known under the name on-line multiplication) up to 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 $ne^{2}[EQUATION]).$ In this paper, 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. In particular, we may take K to be any effective field. We will also present an asymptotically faster algorithm for relaxed multiplication of p-adic numbers.
Starting Page	405
Ending Page	412
Page Count	8
File Format	PDF
ISBN	9781450325011
DOI	10.1145/2608628.2608657
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2014-07-23
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Multiplication Fft On-line algorithm Computer algebra Fundamental algorithms Power series Complexity
Content Type	Text
Resource Type	Article

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Faster relaxed multiplication