Interpolation of track data with radial basis methods
type: Item
instance of: scholarly article
title: Interpolation of track data with radial basis methods
zbMATH Open document ID: 0766.65005
DOI: 10.1016/0898-1221(92)90169-I
author: Thomas A. Foley
author: Ralph E. Carlson
publication date: 1993-04-01T00:00:00Z
review text: The authors study some interpolation problems with data sets \(S\), where \(S=\{(x_ i,y_ i),1\leq i\leq n\}\), of \(n\) distinct points in \(\mathbb{R}^ 2\), in which the points lie along tracks or paths in \(\mathbb{R}^ 2\). Four scattered data interpolation methods that perform well in a critical comparison of \textit{R. Franke} [Math. Comput. 38, 181-200 (1982; Zbl 0476.65005)] are the multiquadric method of \textit{R. L. Hardy} [Comput. Math. Appl. 19, No. 8/9, 163-208 (1990; Zbl 0692.65003)], the thin plate spline method of \textit{J. Duchon} [Lect. Notes Math. 571, 85-100 (1977; Zbl 0342.41012)], the minimum norm network method of \textit{G. M. Nielson} [Math. Comput. 40, 253-271 (1983; Zbl 0549.65005)], and the modified quadratic Shepard method of \textit{R. Franke} and \textit{G. M. Nielson} [Int. J. Numer. Methods Eng. 15, 1691-1704 (1980; Zbl 0444.65011)]. These methods are discussed and applied to several track data samples. Also, the multiquadric and thin plate spline radial basis methods are applied to various sets of data that are sampled densely along tracks in the plane.
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 65D07
zbMATH DE Number: 150165
zbMATH Keywords: scattered data interpolation
zbMATH Keywords: multiquadric method
zbMATH Keywords: thin plate spline method
zbMATH Keywords: minimum norm network method
zbMATH Keywords: quadratic Shepard method
zbMATH Keywords: track data
zbMATH Keywords: radial basis methods
reviewed by: Antonio López-Carmona
describes a project that uses: QSHEP2D
MaRDI profile type: Publication
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published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 150165