English

On Approximating the Riemannian 1-Center

Computational Geometry 2021-04-29 v3

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.

Keywords

Cite

@article{arxiv.1101.4718,
  title  = {On Approximating the Riemannian 1-Center},
  author = {Marc Arnaudon and Frank Nielsen},
  journal= {arXiv preprint arXiv:1101.4718},
  year   = {2021}
}

Comments

23 pages

R2 v1 2026-06-21T17:16:31.325Z