Efficient algorithms for computing univariate relations
(Technical University of Denmark)
Salle XR202 (Bâtiment XLIM)
In this talk, we will present recent results about the fast computation of
univariate relations, including in particular rational interpolants and
Hermite-Pad\'e approximants. Such relations are a central tool in computer
algebra, arising in situations such as the guessing of linear differential
equations, the list-decoding of Reed-Solomon codes, or the computation of
normal forms of polynomial matrices. After giving an overview of the problem
and of existing fast algorithms, the emphasis will be placed on the main ideas
behind the recent algorithmic improvements.
This talk involves joint work with Claude-Pierre Jeannerod, \'Eric Schost,
Gilles Villard, and Vu Thi Xuan.