Explicit error bounds for spline interpolation on a uniform partition
type: Item
instance of: scholarly article
title: Explicit error bounds for spline interpolation on a uniform partition
zbMATH Open document ID: 0835.41015
author: F. Dubeau
author: Jean Savoie
published in: Journal of Approximation Theory
publication date: 1995-09-18T00:00:00Z
review text: The authors have shown that \(C^0_n (u, \upsilon)\) and \(D^0_n (\upsilon)\) are the best constants in the inequalities (1.6) and (1.7) defined on page 3 of this paper. They also present explicit expressions for these constants. In case \(k>0\), they present explicit expressions to bound the constants. Giving some preliminaries, they also establish some useful properties of the kernels \(K^k_n (u, \upsilon, \theta)\). Precisely, this paper considers the optimality and the evaluation of the constants that appear in the expressions of error bounds for interpolating spline functions over a uniform mesh of real line when the nodes are uniformly shifted. Some similar results have already been presented by I. J. Schoenberg in 1976.
Mathematics Subject Classification ID: 41A15
zbMATH DE Number: 782140
zbMATH Keywords: spline interpolation
zbMATH Keywords: error bounds
MaRDI profile type: Publication
full work available at URL: jath.1995.1064
OpenAlex ID: W1974176734
DOI: 10.1006/JATH.1995.1064
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description: scientific article; zbMATH DE number 782140