Worst Cases and Lattice Reduction

Damien Stehlé 1 Vincent Lefèvre 1 Paul Zimmermann 1
1 SPACES - Solving problems through algebraic computation and efficient software
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : We propose a new algorithm to find worst cases for correct rounding of an analytic function. We first reduce this problem to the Real Small Value Problem --- i.e. for polynomials with real coefficients. Then we show that this second problem can be solved efficiently, by extending Coppersmith's work on the Integer Small Value Problem --- for polynomials with integer coefficients --- using lattice reduction. For floating-point numbers with a mantissa less than N, and a polynomial approximation of degree d, our algorithm finds all worst cases at distance $
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https://hal.inria.fr/inria-00099572
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Submitted on : Tuesday, September 26, 2006 - 9:38:49 AM
Last modification on : Thursday, January 11, 2018 - 6:20:00 AM

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Damien Stehlé, Vincent Lefèvre, Paul Zimmermann. Worst Cases and Lattice Reduction. 16th IEEE Symposium on Computer Arithmetic 2003 - ARITH-16'03, 2003, Santiago de Compostela, Espagne, pp.142-147. ⟨inria-00099572⟩

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