The MGPBiCG method for solving the generalized coupled Sylvester-conjugate matrix equations

In this paper, we extend the generalized product-type bi-conjugate gradient (GPBiCG) method for solving the generalized Sylvester-conjugate matrix equations A1XB1+C1Y¯D1=S1,A2X¯B2+C2YD2=S2 by the real representation of the complex matrix and the properties of Kronecker product and vectorization operator. Some numerical experiments demonstrate that the introduced iteration approach is efficient.