Best Rational Approximations with Negative Poles to e to the -x power on (O,infinity).

摘要

In this paper a theory for approximating e(-x) on (O, infinity) with rational functions having negative poles is developed. Numerical results suggest that the best uniform approximation to e(-x) on (O, infinity) from this class has only one pole and this is shown to be the case when using rational functions of this form which are linear polynomials divided by quadratic polynomials. Numerical results are given and compared to recent results of Saff, Schonhage and varga.