On constrained uniform approximation
type: Item
instance of: scholarly article
title: On constrained uniform approximation
zbMATH Open document ID: 1003.41004
DOI: 10.1155/S0161171202012899
author: M. A. Bokhari
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2002-08-13T00:00:00Z
full work available at URL: https://eudml.org/doc/49684
full work available at URL: S0161171202012899.html
review text: Let \(f\) be a function on the unit interval \([0,1]\), and let \(\{x_i\}\) be a finite set of distinct points in \([0,1]\). Let \(m\) be a sufficiently large integer, and let \(S\) be the polynomials of degree \(m\) or less that interpolate to \(f\) on \(\{x_i\}\), and which also have designated higher derivatives that assume prescribed values on \(\{x_i\}\). The general problem is to find the member of \(S\) that is the best uniform approximation to \(f\). The problem, in various forms has a distinguished history that includes classical Hermite interpolation. Here a setting is presented in which the author proves the best approximation is unique.
reviewed by: Daniel Wulbert
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 41A29
Mathematics Subject Classification ID: 41A52
zbMATH DE Number: 1780406
zbMATH Keywords: Hermite interpolation
MaRDI profile type: Publication
OpenAlex ID: W2157265006
description: scientific article; zbMATH DE number 1780406