Certification of the QR factor R and of lattice basis reducedness
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Computing correctly rounded integer powers in floating-point arithmetic
ACM Transactions on Mathematical Software (TOMS)
Speeding-up lattice reduction with random projections
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
SpringSim '10 Proceedings of the 2010 Spring Simulation Multiconference
Rigorous polynomial approximation using taylor models in Coq
NFM'12 Proceedings of the 4th international conference on NASA Formal Methods
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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.