@INPROCEEDINGS{BCEMT2008,
  author = {Brisebarre, Nicolas and Chevillard, Sylvain and Ercegovac, Milos and Muller, Jean-Michel and Torres, Serge},
  title = {{An Efficient Method for Evaluating Polynomial and Rational Function Approximations}},
  booktitle = {{ASAP 08, Conference Proceedings, IEEE 19th International Conference on Application-Specific Systems, Architectures and Processors}},
  year = {2008},
  pages = {233--238},
  address = {Los Alamitos, CA},
  month = {Jul},
  publisher = {IEEE Computer Society},
  hal = {hal-00761652},
  doi = {10.1109/ASAP.2008.4580185},
  abstract = {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.},
  keywords = {Approximation methods, Polynomials, Approximation algorithms, Lattices, Function approximation, Vectors, Accuracy}
}