An efficient method for special least squares solution of the complex matrix equation (AXB,CXD)=(E,F)

In this paper, we propose an efficient method for special least squares solution of the complex matrix equation (AXB,CXD)=(E,F). By using the real representation matrices of complex matrices, the particular structure of the real representation matrices, the Moore-Penrose generalized inverse and the Kronecker product, we obtain the explicit expression of the minimal norm least squares Hermitian solution of the complex matrix equation (AXB,CXD)=(E,F), which was studied by a product of matrices and vectors in Wang et al. (2016). Our resulting formulas only involve real matrices, and the corresponding algorithm only performs real arithmetic. Therefore our proposed method is more effective and portable. Finally, we give three numerical examples to illustrate the effectiveness of our proposed method.