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

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 nonsymmetric 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 A1XB1+C1Y‾D1=E,A2X‾B2+C2YD2=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.