8717
eng
reportzib
0
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2022-06-24
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On Gradient Formulas in an Algorithm for the Logarithm of the Sasaki Metric
The Sasaki metric is the canonical metric on the tangent bundle TM of a Riemannian manifold M. It is highly useful for data analysis in TM (e.g., when one is interested in the statistics of a set of geodesics in M). To this end, computing the Riemannian logarithm is often necessary, and an iterative algorithm was proposed by Muralidharan and Fletcher. In this note, we derive approximation formulas of the energy gradients in their algorithm that we use with success.
1438-0064
urn:nbn:de:0297-zib-87174
publish
Esfandiar Nava-Yazdani
Martin Hanik
Martin Hanik
Felix Ambellan
Christoph von Tycowicz
ZIB-Report
22-12
Computing Methodologies
DIFFERENTIAL GEOMETRY (For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx)
Tycowicz, Christoph von
Ambellan, Felix
Navayazdani, Esfandiar
Hanik, Martin
MathPlus-EF2-3
Visual and Data-centric Computing
https://opus4.kobv.de/opus4-zib/files/8717/Gradient_discrete_log_sasaki.pdf