Minimum norm least-squares solution to general complex coupled linear matrix equations via iteration

Abstract

This paper deals with the problem of finding the minimum norm least-squares solution of a quite general class of coupled linear matrix equations defined over field of complex numbers. To this end, we examine a gradient-based approach and present the convergence properties of the algorithm. The highlight of the elaborated results in the current work is using a new sight of view for construction of the gradient-based algorithm which turns out that we can ignore some of the limitations assumed by the authors in the recently published works for the application of the algorithm to obtain the solution of the referred problems. To the best of our knowledge, so far, computing the optimal convergence factor of the algorithm to determine the (least-squares) solution of general complex linear matrix equations has left as a project to be investigated. In the current work, we determine the optimal convergence factor of the algorithm. Some numerical experiments are reported to illustrate the validity of the presented results.