2016/06/25 by Nattapong Bosuwan, Bosuwan, Nattapong, G. López Lagomasino +1
Mathematics · #30E10 #41A21 #41A28 #Complex Variables (math.CV) #FOS: Mathematics #Fractional Differential Equations Solutions #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials
paper · pdf · doi:10.48550/arxiv.1606.07920
openalex publication_date 2016/06/25 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
Given a system of functions textup\F=(F1,\…,Fd), analytic\non a neighborhood of some compact subset E of the complex plane with simply\nconnected complement, we define a sequence of vector rational functions with\ncommon denominator in terms of the orthogonal expansions of the components\nFk, k=1,\…,d, with respect to a sequence of orthonormal polynomials\nassociated with a measure \μ whose support is contained in E. Such\nsequences of vector rational functions resemble row sequences of type II\nHermite-Pad 'e approximants. Under appropriate assumptions on \μ, we give\nnecessary and sufficient conditions for the convergence with geometric rate of\nthe common denominators of the sequence of vector rational functions so\nconstructed. The exact rate of convergence of these denominators is provided\nand the rate of convergence of the simultaneous approximants is estimated. It\nis shown that the common denominator of the approximants detect the location of\nthe poles of the system of functions.\n