Matrix Approximation by a Sum of Matrix Products

In this paper, we consider solutions of the problems related to the modelling of data transmission systems. Mathematically, the problem is formulated as a problem of approximation of a matrix by a sum of matrix products subject to multiple rank constraints. We provide the solution of this problem in the form of some special iterative procedure and show that iterations converge to a coordinate-wise minimum of the objective function. A particular case of the original problem when the rank constraints are omitted is also considered. In both cases, the solutions are associated with special data transmission systems. The considered problems are extensions of the well-known problems where the matrix approximate is represented by only a single term, not by a sum of matrices.