Some Computational Aspects of a Method for Rational Approximation

Abstract

Numerical aspects of a method for rational approximation of analytic functions on regions in the complex plane are considered. The approximation method divides the problem of computing a rational approximant into three subproblems. First, one chooses a. space of rational functions, then one selects a basis for this space, and finally one determines an element of the space by interpolation. For approximation on regions with bounded simply connected complement, we discuss the choice of space and basis from a numerical point of view. We illustrate with computed examples.