Hermite subdivision with shape constraints on a rectangular mesh
type: Item
instance of: scholarly article
title: Hermite subdivision with shape constraints on a rectangular mesh
zbMATH Open document ID: 1141.65015
author: Jean-Louis Merrien
author: Tom Lyche
published in: BIT
publication date: 2007-01-05T00:00:00Z
review text: In 1999 [Adv. Comput. Math. 10, No. 3-4, 343--365 (1999; Zbl 0934.65009)], \textit{S. Dubuc} and \textit{J.-L. Merrien} introduced a Hermite subdivision scheme which gives \((C^1)\)-interpolants on a rectangular mesh. In this paper a two parameter version of this scheme is analyzed, and \((C^1)\)-convergence is proved for a range of the two parameters. By introducing a control grid the parameters in the scheme can be chosen so that the interpolant inherits positivity and/or directional monotonicity from the initial data. Several examples are given showing that a desired shape can be achieved even if only very crude estimates for the initial slopes are used. The bibliography contains 22 items.
reviewed by: Mykhaylo Pahirya
Mathematics Subject Classification ID: 65D17
Mathematics Subject Classification ID: 65D05
zbMATH DE Number: 5081852
zbMATH Keywords: interpolation
zbMATH Keywords: subdivision
zbMATH Keywords: Hermite date
zbMATH Keywords: rectangular mesh
zbMATH Keywords: positivity
zbMATH Keywords: monotonicity
MaRDI profile type: Publication
full work available at URL: s10543-006-0105-9
OpenAlex ID: W2107666360
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DOI: 10.1007/S10543-006-0105-9
description: scientific article; zbMATH DE number 5081852