Local convergence of Lagrange interpolation associated with equidistant nodes
type: Item
instance of: scholarly article
title: Local convergence of Lagrange interpolation associated with equidistant nodes
zbMATH Open document ID: 0804.41002
author: Xin Li
author: E. B. Saff
published in: Journal of Approximation Theory
publication date: 1994-08-18T00:00:00Z
review text: Let \(f\) be a function defined on \([-1,1]\), \(L_ n( ;\cdot)\) be the Lagrange interpolating polynomial of degree at most \(n\) in the equidistant nodes and let \(G_ s\) denote the interior of level curves \(\Gamma_ s\). The origin of convergence of this polynomial is studied. If \(f\) is bounded on \([-1,1]\) and analytic in \(G_ s\) (without requiring a stronger condition that \(f\) is analytic on \([-1,1]\)), then \(L_ n(f;\cdot)\) converges locally uniformly to \(f\) in \(G_ s\). Consequently if \(f\) is analytic at \(x=0\) and bounded on \([-1,1]\) then the Lagrange interpolants converge to \(f\) in a neighborhood of the origin. Problems to be solved in future are mentioned.
Mathematics Subject Classification ID: 41A05
zbMATH DE Number: 617504
zbMATH Keywords: Lagrange interpolating polynomial
MaRDI profile type: Publication
full work available at URL: jath.1994.1073
OpenAlex ID: W1995663189
DOI: 10.1006/JATH.1994.1073
Recommended article: On Lagrange interpolation with equidistant nodes
Recommended article: On the Divergence of Lagrange Interpolation with Equidistant Nodes
Recommended article: The divergence of Lagrange interpolation in equidistant nodes
Recommended article: Q4009785
Recommended article: Some remarks on the Lagrange interpolation with equidistant nodes
Recommended article: Strong asymptotics in Lagrange interpolation with equidistant nodes
Recommended article: The Lebesgue constant for Lagrange interpolation on equidistant nodes
Recommended article: On Lagrange interpolation with equally spaced nodes
Recommended article: Lebesgue constant for Lagrange interpolation on equidistant nodes
Recommended article: A note on Lagrange interpolation for |x|λ at equidistant nodes
description: scientific article; zbMATH DE number 617504