Numerical Chebyshev Approximation in the Complex Plane

Abstract

The paper describes a numerical method for computing rational approximations of analytic functions on arbitrary simply-connected closed regions of the complex plane. The method is based on approximation on finite point sets and can be regarded as a generalization of the exchange algorithm for real rational approximation. Numerical examples show that for practical purposes, the approximations may be regarded as optimal in the sense of Chebyshev.