Least-Squares Solutions of Generalized Sylvester Equation with Xi Satisfies Different Linear Constraint

In this paper, an iterative method is constructed to find the least-squares solutions of generalized Sylvester equation A X B A X B A X B A X B C 1 1 1 2 2 2 3 3 3 4 4 4 + + + = , where [ ] X X X X 1 2 3 4 , , , is real matrices group, and i X satisfies different linear constraint. By this iterative method, for any initial matrix group ( ) ( ) ( ) ( )     X X X X 0 0 0 0 1 2 3 4 , , , within a special constrained matrix set, a least squares solution group     X X X X     1 2 3 4 , , , with i X satisfying different linear constraint can be obtained within finite iteration steps in the absence of round off errors, and the unique least norm least-squares solution can be obtained by choosing a special kind of initial matrix group. In addition, a minimization property of this iterative method is characterized. Finally, numerical experiments are reported to show the efficiency of the proposed method.