An improved order of approximation for thin-plate spline intepolation in the unit disc
type: Item
instance of: scholarly article
title: An improved order of approximation for thin-plate spline intepolation in the unit disc
zbMATH Open document ID: 0961.41009
author: Yanyan Li
published in: Numerische Mathematik
publication date: 2001-05-17T00:00:00Z
review text: It is proved that for \(1\leq p \leq \infty\) the \(L_p\)-norm of the error of thin-plate spline interpolation to a \(C^\infty\) function in the unit disc decays like \(O(h^{\gamma_p+1/2})\) as \(h\to 0\) with \(\gamma_p:=\min(2,1+2/p)\) when the set \(\Xi\) of interpolation points contains the grid points \(\{hj:j\in Z^2,|hj|<1-h\}\). This improves for the special case of the disc a result of \textit{J. Duchon} [RAIRO, Anal. Numer. 12, 325-334 (1978; Zbl 0403.41003)], who proved for more general regions \(\Omega\) and grids \(\Xi\) the approximation order \(O(\delta^{\gamma_p})\) where \(\delta\) is the distance between \(\Omega\) and \(\Xi\).
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 41A25
Mathematics Subject Classification ID: 41A63
Mathematics Subject Classification ID: 65D07
zbMATH DE Number: 1419743
reviewed by: Rudolf Wegmann
MaRDI profile type: Publication
full work available at URL: s002110050005
OpenAlex ID: W2064172716
DOI: 10.1007/S002110050005
description: scientific article; zbMATH DE number 1419743