Conference PaperOn the approximation of the Riemannian barycenterMataigne, Simon; Absil, P-A; Miolane, NinaWe present a method for computing an approximate Rieman-nian barycenter of a collection of points lying on a Riemannian mani-fold. Our approach relies on the use of theoretically proven under- and over-approximations of the Riemannian distance function. We compare it to Riemannian steepest descent on the exact objective function of the Riemannian barycenter and to an approach that approximates the Rie-mannian logarithm using lifting maps. Experiments are conducted on the Stiefel manifold.7th International Conference on Geometric Science of Information2025-04-2210625575https://doi.org/2240158National Science Foundation