Stability of nonlinear subdivision and multiscale transforms
type: Item
instance of: scholarly article
title: Stability of nonlinear subdivision and multiscale transforms
zbMATH Open document ID: 1225.65028
published in: Constructive Approximation
publication date: 2010-06-09T00:00:00Z
review text: The authors present a new general sufficient condition for the Lipschitz stability of nonlinear subdivision schemes and multiscale transforms in the univariate case. This extends the results of \textit{A. Cohen, N. Dyn} and \textit{B. Matei} [Appl. Comput. Harmon. Anal. 15, No. 2, 89--116 (2003; Zbl 1046.65071)] for the weighted essentially nonoscillatory scheme and the results of \textit{S. Amat} and \textit{J. Liandrat} [Appl. Comput. Harmon. Anal. 18, No. 2, 198--206 (2005; Zbl 1077.65138)] for the piecewise polynomial harmonic transform. With these techniques it is also possible to prove the stability in some new cases (median interpolating transform, power-p schemes, etc.). The results of this paper are also extendable to other nonlinear multiscale transforms like the normal multiresolution and the manifold-valued subdivision and multiscale transforms.
Mathematics Subject Classification ID: 65D18
Mathematics Subject Classification ID: 65T50
Mathematics Subject Classification ID: 26A16
Mathematics Subject Classification ID: 65T60
zbMATH DE Number: 5719084
zbMATH Keywords: nonlinear subdivision and multiscale transforms
zbMATH Keywords: Lipschitz stability
zbMATH Keywords: finite differences
zbMATH Keywords: derived subdivision schemes
zbMATH Keywords: spectral radius conditions
zbMATH Keywords: weighted essentially nonoscillatory scheme
zbMATH Keywords: piecewise polynomial harmonic transform
zbMATH Keywords: median interpolating transform
zbMATH Keywords: power-p schemes
zbMATH Keywords: normal multiresolution
author: Stanislav Harizanov
author: Peter Oswald
MaRDI profile type: Publication
full work available at URL: s00365-010-9082-y
OpenAlex ID: W2070311329
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DOI: 10.1007/S00365-010-9082-Y
description: scientific article; zbMATH DE number 5719084