Multiresolution analysis over triangles, based on quadratic Hermite interpolation
type: Item
instance of: scholarly article
title: Multiresolution analysis over triangles, based on quadratic Hermite interpolation
zbMATH Open document ID: 0962.65119
DOI: 10.1016/S0377-0427(00)00373-3
published in: Journal of Computational and Applied Mathematics
publication date: 2001-05-31T00:00:00Z
review text: Given a triangulation \(T\) of \( \mathbb R^2\), a recipe to build a spline space \(\mathbb S(T)\) over this triangulation, and a recipe to refine the triangulation \(T\) into a triangulation \(T'\), the question arises whether \(\mathbb S(T)\subset \mathbb S(T')\). In this paper the authors discuss how to construct such a nested sequence of spaced based on Powell-Sabin 6-splits for a regular triangulation. The resulting spline space consists of piecewise \(C^1\)-quadratics, and refinement is obtained by subdividing every triangle into four subtriangles at the edge midpoints. The authors develop explicit formulas for wavelet transformations based on quadratic Hermite interpolation, and give a stability result with respect to a natural norm.
reviewed by: Karel Najzar
Mathematics Subject Classification ID: 65T60
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 41A63
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 65D17
Mathematics Subject Classification ID: 65D07
zbMATH DE Number: 1491251
zbMATH Keywords: multivariate splines
zbMATH Keywords: triangulations
zbMATH Keywords: multiresolution analysis
zbMATH Keywords: Hermite interpolation
zbMATH Keywords: wavelet transformations
zbMATH Keywords: stability
author: Morten Dæhlen
author: Tom Lyche
author: Knut Mørken
author: Robert Schneider
author: Hans-Peter Seidel
MaRDI profile type: Publication
cites work: Local decomposition of refinable spaces and wavelets
cites work: Piecewise linear prewavelets on arbitrary triangulations
cites work: Q3839119
cites work: Q4840194
cites work: Piecewise Quadratic Approximations on Triangles
description: scientific article; zbMATH DE number 1491251