Adaptive thinning of centers for approximation of a large data set by radial functions
type: Item
instance of: scholarly article
title: Adaptive thinning of centers for approximation of a large data set by radial functions
zbMATH Open document ID: 1326.41027
author: Pavel Kozlov
author: Nira Dyn
published in: Journal of Approximation Theory
publication date: 2015-09-28T00:00:00Z
review text: Given a bounded set \(D\subset \mathbb{R}^d\), \(d\in \mathbb N\), and a (large) set of centers or points \(\Xi\subset D\), the authors investigate the problem of how to find a small subset \(Y_J\) of \(\Xi\) so that the least squares radial function approximation will be within a given tolerance. The solution the authors offer is based on an adaptive thinning strategy which removes in a greedy way less significant centers in order to minimize the anticipated error. Instead of using the anticipated error, the authors replace it by the new concept of ``predicting functional''. This is a functional which chooses with high probability the same centers as an anticipated error. Several such predicting functionals are derived for specific radial functions. Numerical tests supporting the theoretical findings are also presented.
Mathematics Subject Classification ID: 41A30
Mathematics Subject Classification ID: 65D15
zbMATH DE Number: 6485851
zbMATH Keywords: radial function
zbMATH Keywords: thinning
zbMATH Keywords: anticipated error
zbMATH Keywords: ordering functional
zbMATH Keywords: predicting functional
zbMATH Keywords: functional consistency
reviewed by: Peter Massopust
MaRDI profile type: Publication
full work available at URL: j.jat.2015.07.005
OpenAlex ID: W1429186219
cites work: Radial Basis Functions
cites work: Univariate adaptive thinning
cites work: Adaptive thinning for bivariate scattered data
cites work: Positive powers of certain conditionally negative definite matrices
cites work: Data Dependent Triangulations for Piecewise Linear Interpolation
cites work: Q5689624
cites work: Interpolation of scattered data: distance matrices and conditionally positive definite functions
cites work: Scattered Data Approximation
DOI: 10.1016/J.JAT.2015.07.005
description: scientific article; zbMATH DE number 6485851