June 25, 2007 to June 27, 2007
Nicolas Brisebarre , LaMUSE, Universite J. Monnet, Cedex, France
Sylvain Chevillard , LIP (CNRS/ENS Lyon/INRIA/Univ. Lyon 1), France
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/ARITH.2007.17
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.
Efficient polynomial approximation, floating-point arithmetic, absolute error, L norm, lattice basis reduction, closest vector problem, LLL algorithm.
Nicolas Brisebarre, Sylvain Chevillard, "Efficient polynomial L-approximations", ARITH, 2007, Computer Arithmetic, IEEE Symposium on, Computer Arithmetic, IEEE Symposium on 2007, pp. 169-176, doi:10.1109/ARITH.2007.17