A global approach to the refinement of manifold data

Nira Dyn; Nir Sharon

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arXiv · 1408.3375

A global approach to the refinement of manifold data

Nira Dyn·Nir Sharon

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Abstract

A refinement of manifold data is a computational process, which produces a denser set of discrete data from a given one. Such refinements are closely related to multiresolution representations of manifold data by pyramid transforms, and approximation of manifold-valued functions by repeated refinements schemes. Most refinement methods compute each refined element separately, independently of the computations of the other elements. Here we propose a global method which computes all the refined elements simultaneously, using geodesic averages. We analyse repeated refinements schemes based on this global approach, and derive conditions guaranteeing strong convergence.

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Nira Dyn, Nir Sharon. 2014-08-14. A global approach to the refinement of manifold data. https://arxiv.org/abs/1408.3375

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