Convergence rates of Pade and Pade-type approximants

A comparison is made between Pade and Padi-type approximants. Let Q(n) be the nth orthonormal polynomial with respect to a positive measure mu with compact support in C. We show that for functions of the form f(z) = integral w(t)/z-t d mu(t), where w is an analytic function on the support of mu, Pade-type approximants with denominator Q(n) give a successful and, in general, better approximation procedure than Pade approximation. (C) 1996 Academic Press, Inc.