Sharp error bounds for interpolating splines in tension
type: Item
instance of: scholarly article
title: Sharp error bounds for interpolating splines in tension
zbMATH Open document ID: 0848.41007
DOI: 10.1016/0377-0427(94)00058-9
author: Miljenko Marušić
author: Mladen Rogina
published in: Journal of Computational and Applied Mathematics
publication date: 1995-12-12T00:00:00Z
review text: The authors consider splines in tension of an arbitrary partition of simple knots for the interval \([0, 1]\) with different nonnegative tension parameters on each subinterval. Error bounds are proven for the approximation of a function and its first three derivatives by two different types of interpolatory splines in tension and its respective derivatives: firstly, a \(C^1\) Hermite interpolant determined by function and first derivative values in the knots, and secondly, a \(C^2\) interpolant determined by function values in the knots and two additional endpoint derivative conditions. For these error bounds, the authors derive explicit constants dependent on the tension parameters. In the limiting cases of linear and cubic splines, the constants turn out to be the well-known exact ones for function value estimates by such polynomial splines. For the derivatives, the estimates, though not sharp, are improvements over known results.
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 41A05
zbMATH DE Number: 825291
zbMATH Keywords: splines in tension
zbMATH Keywords: error bounds for interpolation
reviewed by: E. Quak
MaRDI profile type: Publication
full work available at URL: 0377-0427(94)00058-9
OpenAlex ID: W2062705315
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description: scientific article; zbMATH DE number 825291