Joint singular value decomposition algorithm based on the Riemannian trust-region method

抄録

The joint singular value decomposition of multiple rectangular matrices is formulated as a Riemannian optimization problem on the product of two Stiefel manifolds. In this paper, the geometry of the objective function and the Riemannian manifold for this problem are studied to develop a Riemannian trust-region algorithm. The proposed algorithm globally and locally quadratically converges, and our numerical experiments demonstrate that it performs much better than the steepest descent method.