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Article Dans Une Revue LMS Journal of Computation and Mathematics Année : 2012

Medians and means in Finsler geometry

Résumé

We investigate existence and uniqueness of p-means and the median of a probability measure on a Finsler manifold, in relation with the convexity of the support of the measure. We prove that the p-mean is the limit point of a continuous time gradient flow. Under some additional condition which is always satisfied for larger than or equal to 2, a discretization of this path converges to the p-mean. This provides an algorithm for determining those Finsler center points.
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Dates et versions

hal-00540625 , version 1 (28-11-2010)
hal-00540625 , version 2 (24-06-2011)

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Marc Arnaudon, Frank Nielsen. Medians and means in Finsler geometry. LMS Journal of Computation and Mathematics, 2012, 15, pp.23-37. ⟨hal-00540625v2⟩
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