Moving least squares interpolation with thin-plate splines and radial basis functions
type: Item
instance of: scholarly article
title: Moving least squares interpolation with thin-plate splines and radial basis functions
zbMATH Open document ID: 0765.65011
DOI: 10.1016/0898-1221(92)90178-K
publication date: 1993-04-01T00:00:00Z
review text: The author investigates methods based on thin plate splines and on other radial basis functions. It turns out that a small support of the weight function leads to a small support for the spline basis and associated efficiency in the evaluation of the approximant. The moving least squares (MLS) method can then be interpreted as an operator on a function \(f\) generating a certain output. The operator based on polynomials will be denoted \(PMLS\). In general, \(PMLS(f)\) doesn't interpolate \(f\) because \(\dim(P_ m)<n\), where \(P_ m\) is the linear space of bivariate polynomials of degree \(\leq m\). Several examples are given.
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 65D10
Mathematics Subject Classification ID: 41A05
zbMATH DE Number: 150174
zbMATH Keywords: scattered data
zbMATH Keywords: spline basis
zbMATH Keywords: interpolation
zbMATH Keywords: moving least squares method
zbMATH Keywords: thin plate splines
zbMATH Keywords: radial basis functions
author: Kȩstutis Šalkauskas
reviewed by: Antonio López-Carmona
MaRDI profile type: Publication
cites work: Surfaces Generated by Moving Least Squares Methods
cites work: Q3945008
cites work: Q3996207
cites work: Q4110059
cites work: Multivariate interpolation at arbitrary points made simple
cites work: Q4201228
cites work: Q3795136
cites work: Interpolation of scattered data: distance matrices and conditionally positive definite functions
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 150174