A global approach to the refinement of manifold data

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 refineme...

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Bibliographic Details
Published in:Mathematics of computation 2017-01, Vol.86 (303), p.375-395
Main Authors: DYN, NIRA, SHARON, NIR
Format: Article
Language:English
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Summary: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.
ISSN:0025-5718
1088-6842
DOI:10.1090/mcom/3087