Efficient polynomial $L^{\infty}$-approximations

Nicolas Brisebarre (1, 2) , Sylvain Chevillard (1)

1 ARENAIRE - Computer arithmetic
2 LA MUSE - Laboratoire de Mathématiques Unifiées de Saint-Etienne

We address the problem of computing 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.

Mots clés: Efficient polynomial approximation; floating-point arithmetic; absolute error; $L^\infty$ norm; lattice basis reduction; closest vector problem; LLL algorithm

Domaines: Arithmétique des ordinateurs

Nicolas Brisebarre, Sylvain Chevillard. Efficient polynomial $L^{\infty}$-approximations. [Research Report] 2006, pp.11. ⟨inria-00119513v1⟩