Monotone and convex \(C^1\) Hermite interpolants generated by a subdivision scheme
type: Item
instance of: scholarly article
title: Monotone and convex \(C^1\) Hermite interpolants generated by a subdivision scheme
zbMATH Open document ID: 1018.41012
author: Jean-Louis Merrien
author: P. Sablonnière
published in: Constructive Approximation
publication date: 2003-05-04T00:00:00Z
review text: The construction of \(C^1\) monotone and convex interpolants generated by the general subdivision scheme by \textit{J.-L. Merrien} in [Numer. Algorithms 2, 187-200 (1992; Zbl 0754.65011)] was studied. Whatever are the values and slopes of an increasing function \(f\) at the endpoints of a bounded interval \([a,b]\), it is always possible to construct a \(C^1\) increasing Hermite interpolant to \(f\). Similar results hold for a convex \(f\) and convex interpolant to \(f\) and furthermore for decreasing or concave functions \(f\).
Mathematics Subject Classification ID: 41A29
Mathematics Subject Classification ID: 65D17
zbMATH DE Number: 1903847
zbMATH Keywords: Hermite interpolation
zbMATH Keywords: monotone interpolation
zbMATH Keywords: convex interpolation
zbMATH Keywords: approximation with constraints
zbMATH Keywords: modeling of curves
MaRDI profile type: Publication
full work available at URL: s00365-002-0512-3
OpenAlex ID: W354508095
DOI: 10.1007/S00365-002-0512-3
description: scientific article; zbMATH DE number 1903847