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Abstract or Table of Contents
Abstract: "We present a method of enhanced convergence for the approximation of analytic functions. This method introduces conformal transformations in the approximation problems in order to help extract the values of a given analytic function from its Taylor expansion. We show that conformal transformations can extend the radius of convergence of a power series far into infinity, enhance substantially its convergence rates inside the circle of convergence, and can produce a rather dramatic improvement in the conditioning of Pade╠ü approximation. This improvement, which we discuss theoretically for Stieltjes type functions, is most notorious in cases of very poorly conditioned Pade╠ü problems. In some instances, an application of enhanced convergence leads to results which are many orders of magnitude more accurate than those obtained by clasical approximants."