Conjugate gradient least squares algorithm for solving the generalized coupled Sylvester-conjugate matrix equations

In this study, we consider the minimum-norm least squares solution of the generalized coupled Sylvester-conjugate matrix equations by conjugate gradient least squares algorithm. When the system is consistent, the exact solution can be obtained. When the system is inconsistent, the least squares solution can be obtained within finite iterative steps in the absence of round-off error for any initial matrices. Furthermore, we can get the minimum-norm least squares solution by choosing special types of initial matrices. Finally, some numerical examples are given to demonstrate the algorithm considered is quite effective in actual computation.