An Efficient Method for Evaluating Polynomial and Rational Function Approximations - Inria - Institut national de recherche en sciences et technologies du numérique
Communication Dans Un Congrès Année : 2008

An Efficient Method for Evaluating Polynomial and Rational Function Approximations

Résumé

In this paper we extend the domain of applicability of the E-method, as a hardware-oriented method for evaluating elementary functions using polynomial and rational function approximations. The polynomials and rational functions are computed by solving a system of linear equations using digit-serial iterations on simple and highly regular hardware. For convergence, these systems must be diagonally dominant. The E-method offers an efficient way for the fixed-point evaluation of polynomials and rational functions if their coefficients conform to the diagonal dominance condition. Until now, there was no systematic approach to obtain good approximations to f over an interval [a,b] by rational functions satisfying the constraints required by the E-method. In this paper, we present such an approach which is based on linear programming and lattice basis reduction. We also discuss a design and performance characteristics of a corresponding implementation.
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hal-00761652 , version 1 (07-10-2024)

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Nicolas Brisebarre, Sylvain Chevillard, Milos Ercegovac, Jean-Michel Muller, Serge Torres. An Efficient Method for Evaluating Polynomial and Rational Function Approximations. ASAP 08, Jul 2008, Leuven, Belgium. pp.233-238, ⟨10.1109/ASAP.2008.4580185⟩. ⟨hal-00761652⟩
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