Smoothness Equivalence Properties of Manifold‐Valued Data Subdivision Schemes Based on the Projection Approach

DOI10.1137/060652944zbMath1149.26006OpenAlexW2064445894MaRDI QIDQ3507509

Gang Xie, Thomas P.-Y. Yu

Publication date: 19 June 2008

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/060652944

zbMATH Keywords

interpolationsingular value decompositionRiemannian manifoldLie groupsspheresmoothnessapproximation ordernonlinear subdivision schemesclosest point projection\(SO(n)\)linear subdivision schemes

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 (17)

Smoothness equivalence properties of univariate subdivision schemes and their projection analogues ⋮ Single basepoint subdivision schemes for manifold-valued data: time-symmetry without space-symmetry ⋮ On a New Proximity Condition for Manifold-Valued Subdivision Schemes ⋮ Convergence and smoothness analysis of subdivision rules in Riemannian and symmetric spaces ⋮ Hölder regularity of geometric subdivision schemes ⋮ Hermite multiwavelets for manifold-valued data ⋮ Point-normal subdivision curves and surfaces ⋮ Embedding-Based Interpolation on the Special Orthogonal Group ⋮ Invariance property of proximity conditions in nonlinear subdivision ⋮ Geometric Subdivision and Multiscale Transforms ⋮ A necessary and sufficient proximity condition for smoothness equivalence of nonlinear subdivision schemes ⋮ Stability of nonlinear subdivision and multiscale transforms ⋮ Interpolatory wavelets for manifold-valued data ⋮ Nonlinear subdivision through nonlinear averaging ⋮ Locally isometric embeddings of quotients of the rotation group modulo finite symmetries ⋮ $C^1$ Analysis of Hermite Subdivision Schemes on Manifolds ⋮ Approximating the derivative of manifold-valued functions

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