On exact rate of convergence of row sequences of multipoint Hermite-Padé approximants-Reference-Cited by-同舟云学术

On exact rate of convergence of row sequences of multipoint Hermite-Padé approximants

Published:2024-01-01 Issue:1 Volume:57 Page:
ISSN:2391-4661
Container-title:Demonstratio Mathematica
language:en
Short-container-title:

Author:

Bosuwan Nattapong¹²

Affiliation:

1. Department of Mathematics, Faculty of Science, Mahidol University , Rama VI Road, Ratchathewi District , Bangkok 10400 , Thailand

2. Centre of Excellence in Mathematics, CHE, Si Ayutthaya Road , Bangkok 10400 , Thailand

Abstract

Abstract In this article, we analyze a rate of attraction of poles of an approximated function to poles of incomplete multipoint Padé approximants and use it to derive a sharp bound on the geometric rate of convergence of multipoint Hermite-Padé approximants to a vector of approximated functions in the Montessus de Ballore theorem when a table of interpolation points is Newtonian.

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/dema-2023-0140/pdf

Reference18 articles.

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4. E. B. Saff, An extension of Montessus de Ballore’s theorem on the convergence of interpolating rational functions, J. Approx. Theory 6 (1972), 63–67.

5. S. P. Suetin, On the convergence of rational approximations to polynomial expansions in domains of meromorphy of a given function, Math. USSR Sb. 34 (1978), 367–381.