Dual Hermite subdivision schemes of de Rham-type
type: Item
instance of: scholarly article
title: Dual Hermite subdivision schemes of de Rham-type
zbMATH Open document ID: 1335.65022
author: Jean-Louis Merrien
author: Lucia Romani
author: Costanza Conti
published in: BIT
publication date: 2015-01-16T00:00:00Z
review text: The vector subdivision scheme belongs to the iterative algorithms when the resulting refined vector data (containing function values and associated derivatives in the case of Hermite-type data) are obtained from the initial set of vector data by recurrent application of refinement rules. In this paper, a novel method for construction of non-interpolatory Hermite subdivision schemes based on a generalization of the de Rham corner cutting algorithm is presented. The de Rham construction at each subdivision step consists in the double application of an interpolatory Hermite subdivision operator followed by a decimation step selecting only the odd elements of the resulting sequence. Therefore, the de Rham strategy provides Hermite subdivision schemes which are dual by construction, hence approximating the initial data rather than interpolating them. The suggested method is demonstrated on examples, convergence and smoothness investigation including.
reviewed by: Ivana Linkeová
Mathematics Subject Classification ID: 65D17
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 65D10
Mathematics Subject Classification ID: 65D15
zbMATH DE Number: 6387216
zbMATH Keywords: vector subdivision scheme
zbMATH Keywords: Hermite subdivision scheme
zbMATH Keywords: interpolation
zbMATH Keywords: de Rham strategy
zbMATH Keywords: coner cutting algorithm
zbMATH Keywords: dual parametrization
zbMATH Keywords: convergence
zbMATH Keywords: continuity
MaRDI profile type: Publication
full work available at URL: s10543-014-0495-z
OpenAlex ID: W2053830480
cites work: Regularity of multivariate vector subdivision schemes
cites work: Polynomial reproduction for univariate subdivision schemes of any arity
cites work: A new subdivision method for bivariate splines on the four-directional mesh
cites work: Algebraic conditions on non-stationary subdivision symbols for exponential polynomial reproduction
cites work: Dual univariate \(m\)-ary subdivision schemes of de Rham-type
cites work: Interpolatory rank-1 vector subdivision schemes
cites work: Sur une courbe plane
cites work: Hermite subdivision schemes and Taylor polynomials
cites work: Analysis of Hermite-interpolatory subdivision schemes
cites work: Convergence analysis of \(C^{2}\) Hermite interpolatory subdivision schemes by explicit joint spectral radius formulas
cites work: Vector cascade algorithms and refinable function vectors in Sobolev spaces
cites work: Multivariate refinable Hermite interpolant
cites work: Noninterpolatory Hermite subdivision schemes
cites work: A family of Hermite interpolants by bisection algorithms
cites work: Interpolants d'HermiteC2obtenus par subdivision
cites work: A generalized Taylor factorization for Hermite subdivision schemes
cites work: On vector subdivision
cites work: A circle-preserving \(C^{2}\) Hermite interpolatory subdivision scheme with tension control
DOI: 10.1007/S10543-014-0495-Z
description: scientific article; zbMATH DE number 6387216