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Products of ordinary differential operators by evaluation and interpolation

By Alin Bostan, Frédéric Chyzak and Nicolas Le Roux

Abstract

It is known that multiplication of linear differential operators over ground fields of characteristic zero can be reduced to a constant number of matrix products. We give a new algorithm by evaluation and interpolation which is faster than the previously-known one by a constant factor, and prove that in characteristic zero, multiplication of differential operators and of matrices are computationally equivalent problems. In positive characteristic, we show that differential operators can be multiplied in nearly optimal time. Theoretical results are validated by intensive experiments. Categories and Subject Descriptors

Topics: I.1.2 [Computing Methodologies, Symbolic and Algebraic Manipulation – Algebraic Algorithms General Terms, Algorithms, Theory Keywords, Fast algorithms, differential operators
Publisher: ACM Press
Year: 2008
OAI identifier: oai:CiteSeerX.psu:10.1.1.312.9360
Provided by: CiteSeerX
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