A lower bound on the norm of interpolation with an extended Tchebycheff system
type: Item
instance of: scholarly article
title: A lower bound on the norm of interpolation with an extended Tchebycheff system
zbMATH Open document ID: 0599.41007
DOI: 10.1016/0021-9045(86)90032-8
author: Theodore Kilgore
published in: Journal of Approximation Theory
publication date: 1986-01-01T00:00:00Z
review text: For a class of spaces spanned by extended Chebyshev systems defined on a closed interval, the norm of interpolation into a space of dimension \(n+1\) must strictly exceed the norm of optimal Lagrange interpolation into the space of polynomials of degree n-1. As shown by some examples, this fact raises some new questions.
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 41A50
zbMATH DE Number: 3966965
zbMATH Keywords: Chebyshev systems
zbMATH Keywords: optimal Lagrange interpolation
zbMATH Keywords: examples
MaRDI profile type: Publication
full work available at URL: 0021-9045(86)90032-8
OpenAlex ID: W2077706277
cites work: Proof of the conjectures of Bernstein and Erdős concerning the optimal nodes for polynomial interpolation
cites work: Some remarks on polynomials
cites work: Optimization of the norm of the Lagrange interpolation operator
cites work: A characterization of the Lagrange interpolating projection with minimal Tchebycheff norm
cites work: Optimal interpolation with incomplete polynomials
cites work: Optimal interpolation with polynomials having fixed roots
cites work: Q3822645
description: scientific article; zbMATH DE number 3966965