(0,2,3) and (0,1,3) interpolation by six degree splines
type: Item
instance of: scholarly article
title: (0,2,3) and (0,1,3) interpolation by six degree splines
zbMATH Open document ID: 0635.41003
DOI: 10.1016/0377-0427(87)90010-0
author: R. B. Saxena
author: H. C. Tripathi
published in: Journal of Computational and Applied Mathematics
publication date: 1987-01-01T00:00:00Z
review text: Denote by \(S^{(3)}_{m,6}\) the set of all spline functions \(S_{\Delta}\in C^ 3(I)\), \(I=[0,1]\), \(\Delta\) : \(0=x_ 0<...<x_ m=1\), a division of the interval I, such that \(S_{\Delta}\) is a polynomial of degree at most 6 on each interval \([x_{k-1},x_ k]\), \(k=1,2,...,m\). The authors consider two lacunary interpolation problems: Problem (0,2,3) - Find a spline function \(S_{\Delta}\in S^{(3)}_{m,6}\) which interpolates the values of a given function f on I and the values of its derivatives of order 2 and 3, at the knots of \(\Delta\). The problem (0,1,3) is defined similarly. The uniqueness and existence of the solutions of these problems are proved. Estimates of the error of approximation in terms of the modulus of continuity of the sixth derivative \(f^{(6)}\) of f are also given.
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 41A15
zbMATH DE Number: 4034280
zbMATH Keywords: lacunary interpolation
zbMATH Keywords: Estimates
zbMATH Keywords: error of approximation
zbMATH Keywords: modulus of continuity
MaRDI profile type: Publication
full work available at URL: 0377-0427(87)90010-0
OpenAlex ID: W2001016643
cites work: Lakunaere interpolation mit Spline-Funktionen. Die Faelle (0,2,3) und (0,2,4)
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description: scientific article; zbMATH DE number 4034280