Efficient polynomial L-approximations

Montpellier, France June 25-June 27

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

18th IEEE Symposium on Computer Arith ...

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	Nicolas Brisebarre, Sylvain Chevillard, "Efficient polynomial L-approximations," Computer Arithmetic, IEEE Symposium on, pp. 169-176, 18th IEEE Symposium on Computer Arithmetic (ARITH '07), 2007.

	BibTex	x
	@article{ 10.1109/ARITH.2007.17, author = {Nicolas Brisebarre and Sylvain Chevillard}, title = {Efficient polynomial L-approximations}, journal ={Computer Arithmetic, IEEE Symposium on}, volume = {0}, year = {2007}, issn = {1063-6889}, pages = {169-176}, doi = {http://doi.ieeecomputersociety.org/10.1109/ARITH.2007.17}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }

	RefWorks Procite/RefMan/Endnote	x
	TY - CONF JO - Computer Arithmetic, IEEE Symposium on TI - Efficient polynomial L-approximations SN - 1063-6889 SP169 EP176 A1 - Nicolas Brisebarre, A1 - Sylvain Chevillard, PY - 2007 KW - Efficient polynomial approximation KW - floating-point arithmetic KW - absolute error KW - L norm KW - lattice basis reduction KW - closest vector problem KW - LLL algorithm. VL - 0 JA - Computer Arithmetic, IEEE Symposium on ER -

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

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

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," arith, pp.169-176, 18th IEEE Symposium on Computer Arithmetic (ARITH '07), 2007

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