An iterative algorithm for solving the generalized Sylvester-conjugate matrix equation

This paper aims to extend the conjugate gradient least squares method to solve the least squares problem of the generalized Sylvester-conjugate matrix equation. For any initial values, the proposed iterative method can obtain the least squares Frobenius norm solution within finite iteration steps in the absence of roundoff errors. Finally, two numerical examples are given to show the efficiency of the presented iterative method. And it's also proved that our proposed iterative algorithm is better than the existing LSQR iterative algorithm.