Explicit, Nearly Optimal, Linear Rational Approximation with Preassigned Poles

摘要

This paper gives explicit rational functions for interpolating and approximating functions on the intervals -1,1, 0, infinity and -infinity, infinity. The rational functions are linear in the function f to be approximated. The error of approximation of these rationals is nearly as small as the error of best rational approximation with numerator and denominator polynomials of the same degree. Regions of analyticity of f are described, which make it possible to tell a priori, the accuracy which we can expect from rational approximation.