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ADCM
2011

Convergence and smoothness analysis of subdivision rules in Riemannian and symmetric spaces

13 years 6 months ago
Convergence and smoothness analysis of subdivision rules in Riemannian and symmetric spaces
After a discussion on definability of invariant subdivision rules we discuss rules for sequential data living in Riemannian manifolds and in symmetric spaces, having in mind the space of positive definite matrices as a major example. We show that subdivision rules defined with intrinsic means in Cartan-Hadamard manifolds converge for all input data, which is a much stronger result than those usually available for manifold subdivision rules. We also show weaker convergence results which are true in general but apply only to dense enough input data. Finally we discuss C1 and C2 smoothness of limit curves.
Johannes Wallner, Esfandiar Nava Yazdani, Andreas
Added 12 May 2011
Updated 12 May 2011
Type Journal
Year 2011
Where ADCM
Authors Johannes Wallner, Esfandiar Nava Yazdani, Andreas Weinmann
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