On exact rate of convergence of row sequences of multipoint Hermite-Padé approximants

Abstract

In this article, we analyze a rate of attraction of poles of an approximated function to poles of incomplete multipoint Padé approximants and use it to derive a sharp bound on the geometric rate of convergence of multipoint Hermite-Padé approximants to a vector of approximated functions in the Montessus de Ballore theorem when a table of interpolation points is Newtonian.