A Gradient System for Low Rank Matrix Completion

In this article we present and discuss a two step methodology to find the closest low rank completion of a sparse large matrix. Given a large sparse matrix M, the method consists of fixing the rank to r and then looking for the closest rank-r matrix X to M, where the distance is measured in the Frobenius norm. A key element in the solution of this matrix nearness problem consists of the use of a constrained gradient system of matrix differential equations. The obtained results, compared to those obtained by different approaches show that the method has a correct behaviour and is competitive with the ones available in the literature.