Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

Request Permissions   Purchase Content 
 

 

A global approach to the refinement of manifold data


Authors: Nira Dyn and Nir Sharon
Journal: Math. Comp. 86 (2017), 375-395
MSC (2010): Primary 65D99, 40A99, 58E10
DOI: https://doi.org/10.1090/mcom/3087
Published electronically: April 13, 2016
MathSciNet review: 3557803
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2010): 65D99, 40A99, 58E10

Retrieve articles in all journals with MSC (2010): 65D99, 40A99, 58E10


Additional Information

Nira Dyn
Affiliation: School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv, Israel
Email: niradyn@post.tau.ac.il

Nir Sharon
Affiliation: School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv, Israel
Email: Nir.Sharon@math.tau.ac.il

DOI: https://doi.org/10.1090/mcom/3087
Keywords: Manifold data, geodesic average, convergence analysis
Received by editor(s): August 14, 2014
Published electronically: April 13, 2016
Article copyright: © Copyright 2016 American Mathematical Society