A finite iterative algorithm for solving the generalized -reflexive solution of the linear systems of matrix equations

Abstract: In this paper, we proposed an algorithm for solving the linear systems of matrix equations over the generalized -reflexive matrix (). According to the algorithm, the solvability of the problem can be determined automatically. When the problem is consistent over the generalized -reflexive matrix , for any generalized -reflexive initial iterative matrices , the generalized -reflexive solution can be obtained within finite iterative steps in the absence of roundoff errors. The unique least-norm generalized -reflexive solution can also be derived when the appropriate initial iterative matrices are chosen. A sufficient and necessary condition for which the linear systems of matrix equations is inconsistent is given. Furthermore, the optimal approximate solution for a group of given matrices can be derived by finding the least-norm generalized -reflexive solution of a new corresponding linear system of matrix equations. Finally, we present a numerical example to verify the theoretical results of this paper. [Copyright &y& Elsevier]