Rate of pole detection using Padé approximants to polynomial expansions

Abstract Padé approximations constructed from orthogonal and Faber polynomials on some compact set <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>E</m:mi> </m:math> E serve as tools to detect poles of an approximated function around the set <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>E</m:mi> </m:math> E . The goal of this article is to study the rate of such pole detection using indicators introduced by Gonchar ( Poles of rows of the Padé table and meromorphic continuation of functions , Sb. Math. 43 (1981), 527–546). Particularly, we compute the values of these indicators corresponding to our extensions of Padé approximation for the poles of the approximated function within the domain of its meromorphy. Our computations extend the indicator formulas found in the article by Gonchar.