BCR method for solving generalized coupled Sylvester equations over centrosymmetric or anti-centrosymmetric matrix

This paper introduces another version of biconjugate residual method (BCR) for solving the generalized coupled Sylvester matrix equations over centrosymmetric or anti-centrosymmetric matrix. We prove this version of BCR algorithm can find the centrosymmetric solution group of the generalized coupled matrix equations for any initial matrix group within finite steps in the absence of round-off errors. Furthermore, a method is provided for choosing the initial matrices to obtain the least norm solution of the problem. At last, some numerical examples are provided to illustrate the efficiency and validity of methods we have proposed.