Exact values of best approximations for classes of periodic functions by splines of deficiency 2
type: Item
instance of: scholarly article
title: Exact values of best approximations for classes of periodic functions by splines of deficiency 2
zbMATH Open document ID: 1204.41018
DOI: 10.1134/S0001434609030237
published in: Mathematical Notes
publication date: 2009-11-10T00:00:00Z
review text: Let \(X\) be the class of periodic functions whose \(r\)th derivative is a a given rearrangement-invariant set of a class of periodic functions having an \(r\)th derivative whose modulus of continuity is bounded by a given convex function, and let \(m \geq r+1\). For either of these function spaces, the authors provide exact values for the best \(L_1\)-approximations using polynomial splines of order \(m\) and deficiency 2 with equispaced nodes. In addition, these spline spaces are shown to be extremal for the Kolmogorov widths in the function class \(X\).
reviewed by: Kai Diethelm
Mathematics Subject Classification ID: 41A44
Mathematics Subject Classification ID: 41A50
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 41A46
Mathematics Subject Classification ID: 65D07
zbMATH DE Number: 5628181
zbMATH Keywords: periodic function
zbMATH Keywords: best \(L_{1}\)-approximation
zbMATH Keywords: polynomial spline of deficiency 2
zbMATH Keywords: Kolmogorov width
zbMATH Keywords: rearrangement-invariant set
zbMATH Keywords: modulus of continuity
author: V. F. Babenko
author: Nataliia Parfinovych
MaRDI profile type: Publication
cites work: Complexity of approximation problems
cites work: Q5838792
cites work: Inequalities for upper bounds of functionals
cites work: Q3865020
cites work: On n-widths of periodic functions
cites work: Approximations, widths and optimal quadrature formulae for classes of periodic functions with rearrangements invariant sets of derivatives
cites work: Diameters of some classes of differable periodic functions in the space L
cites work: Q3967924
cites work: Q4348446
full work available at URL: s0001434609030237
OpenAlex ID: W1974282175
description: scientific article; zbMATH DE number 5628181