Best error bounds for derivatives in two point Birkhoff interpolation problems
type: Item
instance of: scholarly article
title: Best error bounds for derivatives in two point Birkhoff interpolation problems
zbMATH Open document ID: 0563.41004
DOI: 10.1016/0021-9045(83)90132-6
author: J. Blot
published in: Journal of Approximation Theory
publication date: 1983-01-01T00:00:00Z
review text: Let the real function \(u\in C^{2m}[0,1]\) be given and L be the unique polynomial of degree \(\leq 2m-1\) which interpolates u and its first m-1 even derivatives \(u^{(2j)}\) at 0 and 1. The author gives pointwise bounds of the error u-L and its derivatives in terms of the sup norm of \(u^{(2m)}\) and the Euler polynomials. Further, he proves some particular results on the two point Birkhoff interpolation problems by means of a theorem of Birkhoff and Priver on the same subject.
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 41A25
zbMATH DE Number: 3897514
zbMATH Keywords: Euler polynomials
zbMATH Keywords: two point Birkhoff interpolation problems
reviewed by: Miguel A. Jiménez
MaRDI profile type: Publication
full work available at URL: 0021-9045(83)90132-6
OpenAlex ID: W2081268565
cites work: Hermite Interpolation Errors for Derivatives
cites work: Q5519221
cites work: Numerical methods of high-order accuracy for nonlinear boundary value problems. I: One dimensional problem
cites work: Q3848301
cites work: Completely Convex Functions and Lidstone Series
description: scientific article; zbMATH DE number 3897514