Smoothness Equivalence Properties of General Manifold-Valued Data Subdivision Schemes

DOI10.1137/080718723zbMath1179.26006OpenAlexW1972363811MaRDI QIDQ3182782

Gang Xie, Thomas P.-Y. Yu

Publication date: 16 October 2009

Published in: Multiscale Modeling & Simulation (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/5a3d8ac7e3ff7140acadb55055d59d405724a221

zbMATH Keywords

manifoldsubdivisionsmoothness

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable (26A15) Lipschitz (Hölder) classes (26A16) Interpolation in approximation theory (41A05) Iteration of real functions in one variable (26A18)

Related Items (20)

Stability of manifold-valued subdivision schemes and multiscale transformations ⋮ Single basepoint subdivision schemes for manifold-valued data: time-symmetry without space-symmetry ⋮ Wolfowitz’s theorem and consensus algorithms in Hadamard spaces ⋮ Hermite subdivision on manifolds via parallel transport ⋮ On a New Proximity Condition for Manifold-Valued Subdivision Schemes ⋮ Convergence and smoothness analysis of subdivision rules in Riemannian and symmetric spaces ⋮ Wavelet Sparse Regularization for Manifold-Valued Data ⋮ Invariance property of proximity conditions in nonlinear subdivision ⋮ De Casteljau's algorithm on manifolds ⋮ Subdivision schemes with general dilation in the geometric and nonlinear setting ⋮ On convergent interpolatory subdivision schemes in Riemannian geometry ⋮ Non-smooth Variational Regularization for Processing Manifold-Valued Data ⋮ Geometric Subdivision and Multiscale Transforms ⋮ A necessary and sufficient proximity condition for smoothness equivalence of nonlinear subdivision schemes ⋮ Smoothing nonlinear subdivision schemes by averaging ⋮ Scattered manifold-valued data approximation ⋮ Approximation order from stability for nonlinear subdivision schemes ⋮ Interpolatory wavelets for manifold-valued data ⋮ Clothoid fitting and geometric Hermite subdivision ⋮ $C^1$ Analysis of Hermite Subdivision Schemes on Manifolds

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