Minimally supported error representations and approximation by the constants
type: Item
instance of: scholarly article
title: Minimally supported error representations and approximation by the constants
zbMATH Open document ID: 0954.41003
published in: Numerische Mathematik
publication date: 2000-08-06T00:00:00Z
review text: In this paper the author constructs minimally supported Peano kernel type representations for linear functionals such as the error in multivariate Hermite interpolation. The case of representing the error in approximation to \(f\) by the constant polynomial \(f(a)\) in terms of integrals of the first order derivatives of \(f\) is discussed in detail. It is shown that there exist many representations, which are not minimally supported and involve the integration of first order derivatives over multidimensional regions. Using the representations for the error discussed here the distance of smooth functions from the constants in the uniform norm is estimated.
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 41A44
Mathematics Subject Classification ID: 41A80
Mathematics Subject Classification ID: 41A05
zbMATH DE Number: 1484806
zbMATH Keywords: refinable function
zbMATH Keywords: interpolatory mask
zbMATH Keywords: box splines
zbMATH Keywords: cascade algorithm
author: Shayne Waldron
reviewed by: Ganesh Datta Dikshit
MaRDI profile type: Publication
full work available at URL: s002110000133
OpenAlex ID: W1997329021
DOI: 10.1007/S002110000133
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description: scientific article; zbMATH DE number 1484806