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Smoothness of interpolatory multivariate subdivision in Lie groups

By Philipp Grohs

Abstract

Nonlinear subdivision schemes that operate on manifolds are of use whenever manifold valued data have to be processed in a multiscale fashion. This paper considers the case where the manifold is a Lie group and the nonlinear subdivision schemes are derived from linear interpolatory ones by the so-called log-exp analogy. The main result of the paper is that a multivariate interpolatory Lie group valued subdivision scheme derived from a linear scheme is at least as smooth as the linear scheme, where smoothness is understood in terms of Hölder exponents

Topics: subdivision, nonlinear subdivision, multivariate subdivision
Year: 2008
OAI identifier: oai:CiteSeerX.psu:10.1.1.187.3312
Provided by: CiteSeerX
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