The divergence of the barycentric Pade approximants

Abstract

We explain that, like the usual Padé approximants, the barycentric Padé approximants proposed recently by Brezinski and Redivo-Zaglia can diverge. More precisely, we show that for every polynomial P there exists a power series S, with arbitrarily small coefficients, such that the sequence of barycentric Padé approximants of P + S do not converge uniformly in any subset of the complex plane with a non-empty interior.