Positive sampling in wavelet subspaces
type: Item
instance of: scholarly article
title: Positive sampling in wavelet subspaces
zbMATH Open document ID: 1003.42020
author: Gilbert G. Walter
author: Xiaoping A. Shen
published in: Applied and Computational Harmonic Analysis
publication date: 2002-07-04T00:00:00Z
review text: Properties of the hybrid sampling series in wavelet subspaces are studied. The coefficients in such a series are taken to be sampled values of the function to be approximated, which enables one to avoid the integration arising in the ordinary expansion in a scaling function series. The approximations based on this hybrid series have certain desirable convergence properties: they are locally uniformly convergent for locally continuous functions, they have quadratic uniform convergence rate for functions in certain Sobolev spaces, they are locally bounded when the function is locally bounded and therefore, in particular, Gibbs' phenomenon is avoided. Numerical examples are given to illustrate their results and to compare them with the ordinary expansion.
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 94C10
zbMATH DE Number: 1763731
zbMATH Keywords: positive sampling
zbMATH Keywords: hybrid sampling series
zbMATH Keywords: wavelet subspaces
zbMATH Keywords: approximation
reviewed by: Wenchang Sun
MaRDI profile type: Publication
OpenAlex ID: W2040818573
cites work: Ten Lectures on Wavelets
cites work: The Smith-Barnwell condition and nonnegative scaling functions
cites work: Local convergence for wavelet expansions
cites work: Q4888818
cites work: Modern sampling theory. Mathematics and applications
cites work: Q4381497
cites work: Q4224820
DOI: 10.1006/ACHA.2001.0368
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description: scientific article; zbMATH DE number 1763731