On convergent interpolatory subdivision schemes in Riemannian geometry

DOI10.1007/S00365-014-9264-0zbMath1308.41021OpenAlexW1972420333WikidataQ115388132 ScholiaQ115388132MaRDI QIDQ485354

Yong-Cai Geng, Sumit K. Garg

Publication date: 9 January 2015

Published in: Constructive Approximation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00365-014-9264-0

zbMATH Keywords

convergenceHölder continuityinterpolatory subdivisioninterpolatory waveletssubdivision in Riemannian geometry

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Numerical methods for wavelets (65T60) Rate of convergence, degree of approximation (41A25)

Related Items (8)

Smooth interpolation of key frames in a Riemannian shell space ⋮ Geometric Subdivision and Multiscale Transforms ⋮ Convergence of subdivision schemes on Riemannian manifolds with nonpositive sectional curvature ⋮ Manifold-valued subdivision schemes based on geodesic inductive averaging ⋮ Hyperbolic interpolatory geometric subdivision schemes ⋮ Interpolatory filter banks and interpolatory wavelet packets ⋮ $C^1$ Analysis of Hermite Subdivision Schemes on Manifolds ⋮ A global approach to the refinement of manifold data

Cites Work

• Unnamed Item
• Geometric conditions for tangent continuity of interpolatory planar subdivision curves
• Convergence and smoothness analysis of subdivision rules in Riemannian and symmetric spaces
• Interpolatory wavelets for manifold-valued data
• \(C^1\)-continuity of the generalized four-point scheme
• A 4-point interpolatory subdivision scheme for curve design
• Symmetric iterative interpolation processes
• Interpolation through an iterative scheme
• Definability and stability of multiscale decompositions for manifold-valued data
• Stationary subdivision schemes reproducing polynomials
• Convergence and \(C^1\) analysis of subdivision schemes on manifolds by proximity
• A General Proximity Analysis of Nonlinear Subdivision Schemes
• Smoothness Equivalence Properties of General Manifold-Valued Data Subdivision Schemes
• Smoothness equivalence properties of interpolatory Lie group subdivision schemes
• Stationary subdivision
• Convergence of refinement schemes on metric spaces
• Multiscale Representations for Manifold-Valued Data
• Stochastic Aspects of Nonlinear Refinement Schemes
• Riemannian geometry.

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