2018/01/08 by Nattapong Bosuwan, Bosuwan, N., G. López Lagomasino +1
Mathematics · Physics and Astronomy · #30E10 #41A21 #41A25 #41A27 (Secondary) #41A28 (Primary) #Advanced Mathematical Theories and Applications #Complex Variables (math.CV) #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials
paper · pdf · doi:10.48550/arxiv.1801.03004
openalex publication_date 2018/01/08 · openalex created_date 2018/01/26 · openalex updated_date 2026/07/28
Given a vector function \bf F=(F1,…,Fd), analytic on a neighborhood of some compact subset E of the complex plane with simply connected complement, we define a sequence of vector rational functions with common denominator in terms of the expansions of the components Fk, k=1,…,d, with respect to the sequence of Faber polynomials associated with E. Such sequences of vector rational functions are analogous to row sequences of type II Hermite-Padé approximation. We give necessary and sufficient conditions for the convergence with geometric rate of the common denominators of the sequence of vector rational functions so constructed. The exact rate of convergence of these denominators is provided and the rate of convergence of the approximants is estimated. It is shown that the common denominators of the approximants detect the poles of the system of functions "closest" to E and their order.