Title :
Efficient polynomial L-approximations
Author :
Brisebarre, Nicolas ; Chevillard, Sylvain
Author_Institution :
Univ. J. Monnet, Lyon
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 :
floating point arithmetic; polynomial approximation; floating-point-coefficient polynomial approximation; lattice basis reduction; polynomial Linfin -approximations; supremum norm; Application software; Approximation algorithms; Chebyshev approximation; Computer errors; Floating-point arithmetic; Hardware; Lattices; Least squares approximation; Minimax techniques; Polynomials; Efficient polynomial approximation; L; LLL algorithm.; absolute error; closest vector problem; floating-point arithmetic; lattice basis reduction; norm;
Conference_Titel :
Computer Arithmetic, 2007. ARITH '07. 18th IEEE Symposium on
Conference_Location :
Montepellier
Print_ISBN :
0-7695-2854-6
DOI :
10.1109/ARITH.2007.17
