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arXiv · 1101.4718

On Approximating the Riemannian 1-Center

Marc Arnaudon·Frank Nielsen
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Abstract

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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Marc Arnaudon, Frank Nielsen. 2011-01-25. On Approximating the Riemannian 1-Center. https://doi.org/10.1016/j.comgeo.2012.04.007

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