Rate of system pole detection using Hermite-Padé approximants to polynomial expansions

In this paper, we study the rate at which system poles can be detected via Hermite-Padé approximants constructed from polynomial expansions based on orthogonal and Faber polynomials over a compact set E. Our analysis focuses on certain indicators introduced by Gonchar [13] which quantify the detection of poles by rows of the Padé table. We extend Gonchar’s indicator formulas to our generalized Hermite-Padé approximants and explicitly compute the values of these indicators for the system poles of the vector of approximated functions.