Uniform approximation by the highest defect continuous polynomial splines: Necessary and sufficient optimality conditions and their generalisations
type: Item
instance of: scholarly article
title: Uniform approximation by the highest defect continuous polynomial splines: Necessary and sufficient optimality conditions and their generalisations
zbMATH Open document ID: 1217.90149
author: N. Sukhorukova
published in: Journal of Optimization Theory and Applications
publication date: 2010-12-21T00:00:00Z
review text: The author formulates the problem of polynomial spline approximation as an optimization problem, and then establishes necessary and sufficient optimality conditions for uniform approximation of continuous functions by the highest defect polynomial splines with fixed knots which is a generalization of \textit{Tarashnin}'s theorem [Approximation of the theory of quasidifferentials to solving approximation problems, PhD Thesis, St-Petersburg State University, (1996)]. Necessary and sufficient optimality conditions for polynomial spline approximation with fixed values of the splines at one or both borders of the approximation interval are also derived.
reviewed by: Do Van Luu
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 90C46
zbMATH DE Number: 5828748
zbMATH Keywords: Uniform approximation
zbMATH Keywords: Chebyshev approximation
zbMATH Keywords: polynomial splines with fixed knots
zbMATH Keywords: nonsmooth optimization
zbMATH Keywords: quasidifferentials
MaRDI profile type: Publication
full work available at URL: s10957-010-9715-0
OpenAlex ID: W2001432122
cites work: A class of weak Chebyshev spaces and characterization of best approximations
cites work: Quasidifferentiability and related topics. Dedicated to Prof. Franco Giannessi on his 65th birthday and to Prof. Diethard Pallaschke on his 60th birthday
cites work: Q3995482
cites work: Characterization of Chebyshev Approximations by Splines
DOI: 10.1007/S10957-010-9715-0
description: scientific article; zbMATH DE number 5828748