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Journal Articles Computational Geometry Year : 2013

On Approximating the Riemannian 1-Center


In this paper, we generalize the simple Euclidean 1-center approximation algorithm of Badoiu and Clarkson (2003) to Riemannian geometries and study accordingly the convergence rate. We then show how to instantiate this generic algorithm to two particular cases: (1) hyperbolic geometry, and (2) Riemannian manifold of symmetric positive definite matrices.
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Dates and versions

hal-00560187 , version 1 (27-01-2011)
hal-00560187 , version 2 (30-01-2012)



Marc Arnaudon, Frank Nielsen. On Approximating the Riemannian 1-Center. Computational Geometry, 2013, 46, pp.93-104. ⟨10.1016/j.comgeo.2012.04.007⟩. ⟨hal-00560187v2⟩
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