A Riemannian Limited-memory BFGS Algorithm for Computing the Matrix Geometric Mean
Xinru Yuan, Wen Huang, P.-A. Absil, K. A. Gallivan
Abstract Various optimization algorithms have been proposed to compute the Karcher mean (namely the Riemannian center of mass in the sense of the affine-invariant metric) of a collection of symmetric positive-definite matrices. Here we propose to handle this computational task with a recently developed limited-memory Riemannian BFGS method. We work out an implementation of the method tailored to the symmetric positive-definite Karcher mean problem. We also demonstrate empirically that the method is best suited for large-scale problems in terms of computational time and robustness when comparing to the existing state-of-the-art algorithms.
Proceedings of the International Conference on Computational Science (ICCS), San Diego, California, USA, 6-8 June 2016, to appear, 2016.
- Technical Report
author = "Xinru Yuan and Wen Huang and P.-A. Absil and K. A. Gallivan",
title = "A Riemannian Limited-memory BFGS Algorithm for Computing the Matrix Geometric Mean",
institution = "U.C.Louvain",
number = "UCL-INMA-2015.12",
year = 2015,