(0,2,3) and (0,1,3) interpolation through splines
type: Item
instance of: scholarly article
title: (0,2,3) and (0,1,3) interpolation through splines
zbMATH Open document ID: 0649.41005
DOI: 10.1007/BF01903364
author: R. B. Saxena
author: H. C. Tripathi
published in: Acta Mathematica Hungarica
publication date: 1987-01-01T00:00:00Z
review text: Let \(\Delta:0=x_ 0<x_ 1<...<x_{m-1}<x_ m=1\) be the uniform partition of the interval \(I=[0,1]\) with \(x_ k=k/m\). The authors consider the class \(S_{m,6}^{*(3)}\) of splines \(S_{\Delta}\) which satisfy two conditions; (i) \(S_{\Delta}\in C^ 3(I)\) and (ii) in each interval \([x_ k,x_{k+1}]\), \(S_{\Delta}\in \Pi_ 6\) except in one of the end intervals, say \([x_ 0,x_ 1]\) where \(S_{\Delta}\in \Pi_ 7\). They first prove the existence and uniqueness of splines \(S_{\Delta}\) and \(\tilde S_{\Delta}\in S_{m,6}^{*(3)}\) which satisfy (0,2,3) and (0,1,3) interpolation conditions respectively. They also obtain bounds for the errors \(| S_{\Delta}^{(q)}- f^{(q)}|\) and \(| \tilde S_{\Delta}^{(q)}-f^{(q)}|\), \(q=0,1,...,5\) in the case when \(f\in C^{(6)}(I)\). It would be interesting to compare these with the earlier results of \textit{J. Györvari} [ibid. 42, 25-53 (1983; Zbl 0529.41005)].
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 41A05
zbMATH DE Number: 4060018
zbMATH Keywords: lacunary interpolation problems
reviewed by: A. Sharma
MaRDI profile type: Publication
cites work: Lakunaere interpolation mit Spline-Funktionen. Die Faelle (0,2,3) und (0,2,4)
full work available at URL: https://doi.org/10.1007/bf01903364
OpenAlex ID: W2046939182
description: scientific article; zbMATH DE number 4060018