New Finite Algorithm for Solving the Generalized Nonhomogeneous Yakubovich-Transpose Matrix Equation

In this paper, the development of the conjugate direction (CD) method is constructed to solve the generalized nonhomogeneous Yakubovich-transpose matrix equation AXB + (CXD)-D-T + EYF = R. We prove that the constructed method can obtain the (least Frobenius norm) solution pair (X,Y) of the generalized nonhomogeneous Yakubovich-transpose matrix equation for any (special) initial matrix pair within a finite number of iterations in the absence of round-off errors. Finally, two numerical examples show that the constructed method is more efficient than other similar iterative methods in practical computation.