The coupled Sylvester-transpose matrix equations over generalized centro-symmetric matrices

In this paper, we present an iterative algorithm for solving the following coupled Sylvester-transpose matrix equations q ∑ j=1 ( AijXjBij + CijX j Dij ) = Fi, i = 1, 2, . . . , p, over the generalized centro-symmetric matrix group (X1, X2, . . . , Xq). The solvability of the problem can be determined by the proposed algorithm, automatically. If the coupled Sylvester-transpose matrix equations are consistent over the generalized centro-symmetric matrices, then a generalized centro-symmetric solution group can be obtained within finite iterative steps for any initial generalized centro-symmetric matrix group in the exact arithmetic. Furthermore, it is shown that the least-norm generalized centro-symmetric solution group of the coupled Sylvester-transpose matrix equations can be computed by choosing an appropriate initial iterative matrix group. Moreover, the optimal approximate generalized centro-symmetric solution group to a given arbitrary matrix group (V1, V2, . . . , Vq) can be derived by finding the least-norm generalized centro-symmetric solution group of a new coupled Sylvestertranspose matrix equations. Finally, some numerical results are given to illustrate the validity and practicability of the theoretical results established in this work.