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2008
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An efficient method for evaluating polynomial and rational function approximations

14 years 10 months ago
An efficient method for evaluating polynomial and rational function approximations
In this paper we extend the domain of applicability of the E-method [7, 8], 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.
Nicolas Brisebarre, Sylvain Chevillard, Milos D. E
Added 12 Oct 2010
Updated 12 Oct 2010
Type Conference
Year 2008
Where ASAP
Authors Nicolas Brisebarre, Sylvain Chevillard, Milos D. Ercegovac, Jean-Michel Muller, Serge Torres
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