A uniform approach for Hermite Padé and simultaneous Padé approximants and their matrix-type generalizations

Abstract

This paper introduces the notion of apower Hermite Pade approximant, a generalization of the classical scalar Hermite Pade approximant. We show that this generalized form provides a unifor approach for different concepts of matrix-type Pade approximants. This includes descriptions of vector and matrix Pade approximants along with generalizations of simultaneous and Hermite Pade approximants.