Approximation order from stability for nonlinear subdivision schemes

DOI10.1016/j.jat.2009.12.003zbMath1196.65041OpenAlexW2137994890MaRDI QIDQ976206

Philipp Grohs

Publication date: 17 June 2010

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jat.2009.12.003

zbMATH Keywords

stabilityLie groupapproximation ordernonlinear subdivision schemeRiemann metric

Mathematics Subject Classification ID

Numerical aspects of computer graphics, image analysis, and computational geometry (65D18)

Related Items (8)

Stability of manifold-valued subdivision schemes and multiscale transformations ⋮ Nonlinear multi-scale transforms: \(L_{p}\) theory ⋮ Optimal a priori discretization error bounds for geodesic finite elements ⋮ Geometric multiscale decompositions of dynamic low-rank matrices ⋮ Geometric Subdivision and Multiscale Transforms ⋮ Scattered manifold-valued data approximation ⋮ A class of nonlinear four-point subdivision schemes ⋮ Approximating the derivative of manifold-valued functions

Cites Work

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• Stability of manifold-valued subdivision schemes and multiscale transformations
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• Stability of nonlinear subdivision and multiscale transforms
• Some results on uniformly high-order accurate essentially nonoscillatory schemes
• Smoothness of nonlinear median-interpolation subdivision
• Interpolation through an iterative scheme
• Normal multiresolution approximation of curves
• Analysis of a class of nonlinear subdivision schemes and associated multiresolution transforms
• Convergence and \(C^1\) analysis of subdivision schemes on manifolds by proximity
• Smoothness Equivalence Properties of General Manifold-Valued Data Subdivision Schemes
• Stationary subdivision
• Nonlinear Pyramid Transforms Based on Median-Interpolation

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