The matrix iterative methods for solving a class of generalized coupled Sylvester-conjugate linear matrix equations

摘要

The conjugate gradients-squared (CGS) method (Sonneveld, 1989) has been considered as an efficient variant of the bi-conjugate gradient (BCG) method. In Vorst (1992), a more smoothly converging variant of the BCG method which keeps the attractive convergence rate of the CGS method was investigated for the solution of certain classes of nonsymmet-ric linear systems, so-called bi-conjugate gradient stabilized (Bi-CGSTAB) method. In this paper, we will combine these interesting methods for solving the generalized coupled Sylvester-conjugate matrix equations A_1XB_1 +C_1YD_1 = E, A_2XB_2 +C_2YD_2 = F after performing suitable transformation by the properties of Kronecker product and vec operator. Some numerical experiments demonstrate that the introduced iterative methods are more efficient than the existing methods.