Generalized interpolating refinable function vectors
type: Item
instance of: scholarly article
title: Generalized interpolating refinable function vectors
zbMATH Open document ID: 1166.65069
author: Bin Han
author: Soon-Geol Kwon
author: Xiaosheng Zhuang
published in: Journal of Computational and Applied Mathematics
publication date: 2009-04-29T00:00:00Z
review text: Compactly supported interpolating \(d\)-refinable function vectors with any dilation factor \(d>1\) are considered. Motivated by wavelet applications, it is desirable to have compactly supported refinable functions that are both interpolating and orthogonal. But it is impossible to have a compactly supported scalar 2-refinable function such that it is both interpolating and orthogonal.Therefore it is natural to consider \(d\)-refinable function vectors. The authors characterize both interpolating \(d\)-refinable function vectors and orthogonal interpolating \(d\)-refinable function vectors in terms of their masks and study their approximation properties. A family of interpolatory masks for compactly supported interpolating \(d\)-refinable function vectors with increasing orders of sum rules is presented. Several examples of compactly supported (orthogonal) interpolating refinable function vectors and biorthogonal multiwavelets derived from such interpolating function vectors are given.
reviewed by: Manfred Tasche
Mathematics Subject Classification ID: 65T60
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 42C15
zbMATH DE Number: 5549324
zbMATH Keywords: interpolating refinable function vectors
zbMATH Keywords: compactly supported refinable function vectors
zbMATH Keywords: dilation factor
zbMATH Keywords: orthogonal interpolating refinable function vectors
zbMATH Keywords: sum rules
zbMATH Keywords: biorthogonal multiwavelets
zbMATH Keywords: CBC algorithm
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
full work available at URL: j.cam.2008.03.014
OpenAlex ID: W1997381877
cites work: Construction of multivariate biorthogonal wavelets with arbitrary vanishing moments
cites work: Ten Lectures on Wavelets
cites work: Symmetric iterative interpolation processes
cites work: Symmetric orthonormal scaling functions and wavelets with dilation factor 4
cites work: Analysis and Construction of Optimal Multivariate Biorthogonal Wavelets with Compact Support
cites work: Approximation properties and construction of Hermite interpolants and biorthogonal multiwavelets
cites work: Symmetry property and construction of wavelets with a general dilation matrix
cites work: Vector cascade algorithms and refinable function vectors in Sobolev spaces
cites work: Solutions in Sobolev spaces of vector refinement equations with a general dilation matrix
cites work: The structure of balanced multivariate biorthogonal multiwavelets and dual multiframelets
cites work: Multivariate Refinement Equations and Convergence of Subdivision Schemes
cites work: Multiwavelet frames from refinable function vectors
cites work: On linear independence for integer translates of a finite number of functions
cites work: INTERPOLATING SCALING VECTORS
cites work: Interpolating multiwavelet bases and the sampling theorem
cites work: Interpolatory orthogonal multiwavelets and refinable functions
DOI: 10.1016/J.CAM.2008.03.014
description: scientific article; zbMATH DE number 5549324