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  <doc>
    <id>8717</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2022-06-24</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">On Gradient Formulas in an Algorithm for the Logarithm of the Sasaki Metric</title>
    <abstract language="eng">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.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-87174</identifier>
    <enrichment key="opus.source">publish</enrichment>
    <author>Esfandiar Nava-Yazdani</author>
    <submitter>Martin Hanik</submitter>
    <author>Martin Hanik</author>
    <author>Felix Ambellan</author>
    <author>Christoph von Tycowicz</author>
    <series>
      <title>ZIB-Report</title>
      <number>22-12</number>
    </series>
    <collection role="ccs" number="I.">Computing Methodologies</collection>
    <collection role="msc" number="53-XX">DIFFERENTIAL GEOMETRY (For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx)</collection>
    <collection role="persons" number="vontycowicz">Tycowicz, Christoph von</collection>
    <collection role="persons" number="ambellan">Ambellan, Felix</collection>
    <collection role="persons" number="navayazdani">Navayazdani, Esfandiar</collection>
    <collection role="persons" number="hanik">Hanik, Martin</collection>
    <collection role="projects" number="MathPlus-EF2-3">MathPlus-EF2-3</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/8717/Gradient_discrete_log_sasaki.pdf</file>
  </doc>
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