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 Sigma(q)(j=1)(A(ij)X(j)B(ij) + (CijXjDij)-D-T) = F-i, i = 1, 2, ..., p, over the generalized centro-symmetric matrix group (X-1, X-2, ..., X-q). 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 (V-1, V-2, ..., V-q) can be derived by finding the least-norm generalized centro-symmetric solution group of a new coupled Sylvester-transpose matrix equations. Finally, some numerical results are given to illustrate the validity and practicability of the theoretical results established in this work.