A Note on the Rate of Convergence of Poles of Generalized Hermite-Pade Approximants

Nattapong Bosuwan

Abstract

We consider row sequences of three generalized Hermite-Pade approximations (orthogonal Hermite-Pade approximation, Hermite-Pade-Faber approximation, and multipoint Hermite-Pade approximation) of a vector of the approximated functions F and prove that if F has a system pole of order ν, then such system pole attracts at least ν zeros of denominators of these approximants at the rate of a geometric progression. Moreover, the rates of these attractions are estimated.