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In this paper, we present dynamical systems for computing the low rank approximation of a single matrix and of a set of matrices. These dynamical systems arise from solving an optimization problem involving these matrices. The proposed methods are based on applying smooth optimization techniques on smooth manifolds. Many of these systems are then modified to obtain power-like methods for computing...
Multiplicative update algorithms have proved to be a great success in solving optimization problems with nonnegativity constraints, such as the famous nonnegative matrix factorization (NMF) and its many variants. However, despite several years of research on the topic, the understanding of their convergence properties is still to be improved. In this paper, we show that Lyapunov's stability theory...
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