Proof of convergence of an iterative technique for thin plate spline interpolation in two dimensions
type: Item
instance of: scholarly article
title: Proof of convergence of an iterative technique for thin plate spline interpolation in two dimensions
zbMATH Open document ID: 0944.65015
DOI: 10.1023/A:1018923925800
author: A. C. Faul
author: M. J. D. Powell
published in: Advances in Computational Mathematics
publication date: 2000-09-13T00:00:00Z
review text: The paper studies the thin plate spline solution of the interpolation problem \(s(x_i) = f_i\), \(i=1,\dots,n\), where \(x_i \in \mathbb{R}^2\), \(f_i \in \mathbb{R}\) are data and the points \(x_i\) are required to be all different and not collinear. A generalization of the iterative algorithm described by \textit{M. J. D. Powell} [Ann. Numer. Math. 4, No. 1-4, 519-527 (1997; Zbl 0885.65012)] is presented, and a convergence proof of this method is given. The interpolation method and the analysis also apply to radial basis functions and to other functions that are conditionally positive definite. The speed of convergence of the method is shown by some numerical results.
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 65D05
zbMATH DE Number: 1407666
zbMATH Keywords: thin plate spline interpolation
zbMATH Keywords: iterative algorithm
zbMATH Keywords: convergence
zbMATH Keywords: radial basis functions
zbMATH Keywords: numerical examples
reviewed by: Johannes Elschner
MaRDI profile type: Publication
full work available at URL: a:1018923925800
OpenAlex ID: W104736067
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description: scientific article; zbMATH DE number 1407666