On divergence of Hermite-Fejér interpolation to \(f(z)=z\) in the complex plane
type: Item
instance of: scholarly article
title: On divergence of Hermite-Fejér interpolation to \(f(z)=z\) in the complex plane
zbMATH Open document ID: 0939.41005
author: Yanyan Li
published in: Constructive Approximation
publication date: 2000-02-03T00:00:00Z
review text: The aim of this paper is the following result: Let \(X= \{x^n_k\}\), \(n\in\{1,2,\dots\}\), \(k\in 1,\dots, n\), \(-1\leq x^{(n)}_1<\cdots< x^{(n)}_n\leq 1\), be an interpolatory matrix of nodes coinciding with the roots of the polynomials which are orthogonal on \([-1,1]\) with respect to an arbitrary summable, almost everywhere positive, weight function. Then \(\lim_{n\to\infty}|r_{2n-1}(z)|= \infty\), \(z\not\in [-1,1]\), where \(r_{2n-1}(z)= z- H_{2n-1}(z)\) and \(H_{2n-1}(f, x;z)\) are the Hermite-Fejér interpolating polynomials.
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 41A10
zbMATH DE Number: 1398364
zbMATH Keywords: divergence
zbMATH Keywords: Hermite-Fejér interpolating
reviewed by: Ion Badea
MaRDI profile type: Publication
full work available at URL: s003659900124
OpenAlex ID: W2027699829
DOI: 10.1007/S003659900124
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description: scientific article; zbMATH DE number 1398364