Iterative solutions to matrix equations of form

To solve systems of linear matrix equations A₁XB₁ = F₁ and A₂XB₂ = F₂, we present iterative algorithms to get the solutions. For any initial value, we prove that the iterative solutions consistently converge to the true one. The proposed algorithms are concerned on new iterative solutions to the equations under some condition. Finally, a simulation example is given and the results verify the theoretical findings.