Froissart doublets in Padé approximation in the case of polynomial noise

摘要

First, we study the relation between the zeros of random polynomials Rn+1 and the zeros and poles of their Padé approximants [n/n]Rn+1. Next, we consider the distribution of zeros and poles of Padé approximants to the geometric series perturbed by a random polynomial noise. We observe numerically interesting connections between two above problems. Some numerical observations on the Froissart doublets have been also made.