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On Gradient Formulas in an Algorithm for the Logarithm of the Sasaki Metric

Please always quote using this URN: urn:nbn:de:0297-zib-87174
  • 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.

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Author:Esfandiar Nava-Yazdani, Martin HanikORCiD, Felix AmbellanORCiD, Christoph von Tycowicz
Document Type:ZIB-Report
MSC-Classification:53-XX DIFFERENTIAL GEOMETRY (For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx)
CCS-Classification:I. Computing Methodologies
Date of first Publication:2022/06/24
Series (Serial Number):ZIB-Report (22-12)
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