Radial basis functions for the multivariate interpolation of large scattered data sets
type: Item
instance of: scholarly article
title: Radial basis functions for the multivariate interpolation of large scattered data sets
zbMATH Open document ID: 1025.65015
DOI: 10.1016/S0377-0427(01)00485-X
published in: Journal of Computational and Applied Mathematics
publication date: 2002-06-24T00:00:00Z
review text: The authors present an improved version of \textit{D. Shepard}'s radial basis function (RBF) method [A two-dimensional interpolation function for irregularly spaced data, Proceeding of rthe 23rd National Conference, ACM, 517-523 (1968)] using a local interpolation, i.e. compactly supported RBF as nodal functions. This provides the efficiency and reproduction quality and also optimizes the implementation of the multivariate interpolation software of large (several thousand points) scattered data sets given by \textit{R. J. Renka} [ACM Trans. Math. Softw. 14, 149-150 (1988; Zbl 0709.65504); ibid. 14, 151-152 (1988; Zbl 0709.65502)]. The numerical tests for bi-variate and tri-variate interpolation show that the localisation of RBF outperforms the multilevel method in the case, when the number of samples is large.
reviewed by: Jacek Gilewicz
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 41A63
Mathematics Subject Classification ID: 65Y20
zbMATH DE Number: 1758445
zbMATH Keywords: multivariate interpolation
zbMATH Keywords: improvement of numerical algorithms
zbMATH Keywords: scattered data
zbMATH Keywords: numerical examples
zbMATH Keywords: performance
zbMATH Keywords: radia basis function method
zbMATH Keywords: local interpolation
zbMATH Keywords: multilevel method
author: D. Lazzaro
author: Laura B. Montefusco
describes a project that uses: QSHEP2D
describes a project that uses: QSHEP3D
describes a project that uses: Algorithm 792
MaRDI profile type: Publication
cites work: Multistep scattered data interpolation using compactly supported radial basis functions
cites work: Scattered Data Interpolation: Tests of Some Method
cites work: Smooth interpolation of large sets of scattered data
cites work: A Parallel Multivariate Interpolation Algorithm With Radial Basis Functions
cites work: Multilevel interpolation and approximation
cites work: Multivariate interpolation of large sets of scattered data
cites work: Algorithm 660: QSHEP2D: Quadratic Shepard Method for Bivariate Interpolation of Scattered Data
cites work: Algorithm 661
cites work: Algorithm 792
cites work: A triangle-based \(C^ 1\) interpolation method
cites work: Q4856431
cites work: Error estimates and condition numbers for radial basis function interpolation
cites work: Error estimates for interpolation by compactly supported radial basis functions of minimal degree
cites work: Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree
cites work: Compactly supported positive definite radial functions
full work available at URL: s0377-0427(01)00485-x
OpenAlex ID: W2069016826
description: scientific article; zbMATH DE number 1758445