Restricted nonlinear approximation
type: Item
instance of: scholarly article
title: Restricted nonlinear approximation
zbMATH Open document ID: 0947.41006
author: Ronald DeVore
author: Reinhard Hochmuth
author: Albert Cohen
published in: Constructive Approximation
publication date: 2000-11-05T00:00:00Z
review text: This paper introduces a new form of nonlinear approximation called restricted approximation. It is a generalization of \(n\)-term wavelet approximation in which a weight function is used to control the terms in the wavelet expansion of the approximant. This form of approximation occurs in statistical estimation and in the characterization of interpolation spaces for certain pairs of \(L_p\) and Besov spaces. This paper characterizes, both in terms of their wavelet coefficients and also in terms of their smoothness, the functions which are approximated with a specified rate by restricted approximation. This paper also shows the relation of this form of approximation with certain types of thresholding of wavelet coefficients.
reviewed by: Yingguang Shi
Mathematics Subject Classification ID: 41A17
Mathematics Subject Classification ID: 41A25
Mathematics Subject Classification ID: 41A46
zbMATH DE Number: 1419735
zbMATH Keywords: restricted approximation
zbMATH Keywords: nonlinear approximation
zbMATH Keywords: characterization of approximation classes
zbMATH Keywords: Besov spaces
zbMATH Keywords: \(K\)-functionals
MaRDI profile type: Publication
full work available at URL: s003659910004
OpenAlex ID: W2043997216
Wikidata QID: Q127674044
DOI: 10.1007/S003659910004
description: scientific article; zbMATH DE number 1419735