@INPROCEEDINGS{BrisebarreChevillard2007, author = {N.~Brisebarre and S.~Chevillard}, title = {Efficient polynomial ${L}^{\infty}$-approximations}, booktitle = {18th IEEE SYMPOSIUM on Computer Arithmetic}, year = {2007}, editor = {P.~Kornerup and J.-M.~Muller}, pages = {169--176}, address = {Los Alamitos, CA}, month = {June}, publisher = {IEEE Computer Society}, 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.}, keywords = {Efficient polynomial approximation, floating-point arithmetic, absolute error, $L^\infty$ norm, lattice basis reduction, closest vector problem, LLL algorithm.} }