Global least squares method based on tensor form to solve linear systems in Kronecker format

Abstract

In this paper, we propose a new algorithm based on the global least squares method for solving linear systems in Kronecker format. Because of the inefficiency of iterative methods for solving linear systems in Kronecker format in high dimensions, we consider the tensor form of these systems and apply the global least squares method based on the tensor form to obtain an approximate solution. We use the new method to solve the Sylvester tensor equations in Kronecker format, as a special case of these systems. The convergence analysis of the new method is also investigated. Numerical results demonstrate the efficiency of the new method in comparison with some existing methods.