Convergence of derivatives of optimal nodal splines
type: Item
instance of: scholarly article
title: Convergence of derivatives of optimal nodal splines
zbMATH Open document ID: 0870.41008
author: V. Demichelis
published in: Journal of Approximation Theory
publication date: 1997-05-05T00:00:00Z
review text: In this paper the author studies the problem of convergence of derivatives of optimal nodal splines. Optimal nodal spline interpolants \(Wf\) of order \(m\) which have local support can be used to interpolate a continuous function \(f\) at a set of mesh points. The author provides a set of sufficient conditions for a sequence of locally uniform meshes for the uniform convergence of \(D^jWf\) to \(D^jf\) for \(f\in {\mathcal C}^s\) and \(j=1,2\) \(s<m\). He also gives a bound for \(D^rWf\) with \(s<r<m\). Further he uses optimal nodal spline interpolations for the numerical evaluation of Cauchy principal value integrals.
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 65D05
zbMATH DE Number: 1006711
zbMATH Keywords: Cauchy principal value integrals
zbMATH Keywords: spline approximation
zbMATH Keywords: optimal nodal spline
zbMATH Keywords: spline interpolations
reviewed by: Ganesh Datta Dikshit
MaRDI profile type: Publication
full work available at URL: jath.1996.3012
OpenAlex ID: W2019464731
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DOI: 10.1006/JATH.1996.3012
description: scientific article; zbMATH DE number 1006711