Symmetric solution to matrix equation with conjugate and transpose unknown and its application in control

In this paper, we consider the the symmetric least squares solution to a kind of matrix equation with conjugate and transpose unknown by applying of a modified conjugate gradient least, squares iterative algorithm, which is called on the MCGLS iterative algorithm. In addition, the convergence analysis of the algorithm is proven. Moreover, two examples are offered at the end of this paper for showing the feasible of the MCGLS iterative algorithm.