On uniform convergence of rational, Newton-Padé interpolants of type (n,n) with free poles as \(n\to \infty\)
type: Item
instance of: scholarly article
title: On uniform convergence of rational, Newton-Padé interpolants of type (n,n) with free poles as \(n\to \infty\)
zbMATH Open document ID: 0685.41003
DOI: 10.1007/BF01390053
published in: Numerische Mathematik
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133354
review text: Let f be a meromorphic function in the complex plane \({\mathbb{C}}\). The author shows that there exists a sequence of distinct interpolation points \(\{z_ i\}_{i=1,2,...}\), and for \(n\geq 1\), rational functions \(R_ n(z)\) of type (n,n) solving the Newton-Padé (Hermite) interpolation problem, \(R_ n(z_ i)=f(z_ i),\) \(i=1,2,...,2n+1\), such that for each compact subset K of \({\mathbb{C}}\) except the poles of f, it holds that \(\lim_{n\to \infty}\| f-R_ n\|^{1/n}_{L_{\infty}(K)}=0.\) And the author discusses some extended and related results in the case that f(z) is meromorphic in a given open set with certain additional conditions.
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 41A20
Mathematics Subject Classification ID: 41A21
Mathematics Subject Classification ID: 30E10
zbMATH DE Number: 4122538
zbMATH Keywords: Newton-Padé interpolation
zbMATH Keywords: Hermite interpolation
zbMATH Keywords: meromorphic function
author: Doron S. Lubinsky
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4122538