Computer Arithmetic, IEEE Symposium on (2007)

Montpellier, France

June 25, 2007 to June 27, 2007

ISSN: 1063-6889

ISBN: 0-7695-2854-6

pp: 169-176

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/ARITH.2007.17

Nicolas Brisebarre , LaMUSE, Universite J. Monnet, Cedex, France

Sylvain Chevillard , LIP (CNRS/ENS Lyon/INRIA/Univ. Lyon 1), France

ABSTRACT

We address the problem of computing a good floating-point-coefficient polynomial approximation to a function, with respect to the supremum norm. This is a key step in most processes of evaluation of a function. We present a fast and efficient method, based on lattice basis reduction, that often gives the best polynomial possible and most of the time returns a very good approximation.

INDEX TERMS

Efficient polynomial approximation, floating-point arithmetic, absolute error, L norm, lattice basis reduction, closest vector problem, LLL algorithm.

CITATION

Nicolas Brisebarre,
Sylvain Chevillard,
"Efficient polynomial L-approximations",

*Computer Arithmetic, IEEE Symposium on*, vol. 00, no. , pp. 169-176, 2007, doi:10.1109/ARITH.2007.17