Filter bank algorithms for piecewise linear prewavelets on arbitrary triangulations
type: Item
instance of: scholarly article
title: Filter bank algorithms for piecewise linear prewavelets on arbitrary triangulations
zbMATH Open document ID: 0962.65120
DOI: 10.1016/S0377-0427(00)00378-2
author: Michael S. Floater
author: E. Quak
author: M. Reimers
published in: Journal of Computational and Applied Mathematics
publication date: 2001-05-31T00:00:00Z
review text: This paper concerns the practical aspects of using piecewise linear prewavelets over triangulations for decomposition, reconstruction, and approximation via thresholding. The authors show that the Schur complement of the associated two scale matrix is symmetric, positive definite, and well conditioned. This paper is completed with two numerical examples of decomposition, reconstruction, and thresholding both when applying the prewavelet basis and when using the Faber decomposition scheme. In addition the authors compute the condition numbers of the Schur complements for prewavelet decomposition.
reviewed by: Karel Najzar
Mathematics Subject Classification ID: 65T60
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 65F35
zbMATH DE Number: 1491256
zbMATH Keywords: wavelets space
zbMATH Keywords: prewavelets
zbMATH Keywords: splines
zbMATH Keywords: triangulations
zbMATH Keywords: filter bank algorithms
zbMATH Keywords: Schur complements
zbMATH Keywords: condition number
zbMATH Keywords: decomposition
zbMATH Keywords: reconstruction
zbMATH Keywords: thresholding
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
cites work: Q3208805
cites work: Multiresolution analysis over triangles, based on quadratic Hermite interpolation
cites work: Piecewise linear prewavelets on arbitrary triangulations
cites work: Q4240355
cites work: Linear Independence and Stability of Piecewise Linear Prewavelets on Arbitrary Triangulations
cites work: Scattered Data Interpolation: Tests of Some Method
cites work: Methods of conjugate gradients for solving linear systems
cites work: Q4259925
cites work: Macro-elements and stable local bases for splines on Powell-Sabin triangulations
cites work: Q4840194
cites work: Q4246998
cites work: Q3143213
cites work: On the multi-level splitting of finite element spaces
full work available at URL: s0377-0427(00)00378-2
OpenAlex ID: W1982118128
description: scientific article; zbMATH DE number 1491256