Least squares Hermitian solution of the complex matrix equation AXB+CXD=E with the least norm

In this paper, a new method is presented to solve the least squares Hermitian problem of the complex matrix equation AXB+CXD=E. The explicit expression of least squares Hermitian solution with the least norm is given. The least squares Hermitian solution with the least norm of complex matrix equation AXB=E is also derived. Numerical algorithms and numerical examples show the feasibility of our method.