A Riemannian Limited-memory BFGS Algorithm for Computing the Matrix Geometric Mean


Xinru Yuan, Wen Huang, P.-A. Absil, K. A. Gallivan


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.


Procedia Computer Science, 80:2147-2157, 2016.


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