Studies On Iterative Method For Solving The Generalized Coupled Sylvester Matrix Equations

Linear system theory has an important role in the generalized coupling matrix equations (such as generalized coupled Sylvester matrix equations (AXB+CYD,EXF+GYH)= (M,N), etc.), and research on the coupling matrix equations (including the least squares solution) method has been carried out for many years. When using Kronecker product as a method for solving linear equations, traditionally, solving the large matrix will take up a lot of memory and result in solving difficult due to the need to use the inverse matrix. So an iterative solution method began to appear.This thesis studies the iterative solution of the generalized coupled Sylvester matrix equations. Firstly, an iterative method has been introduced, focusing on the generalized reflexive solutions and optimal approximation solutions of the generalized coupled Sylvester matrix equations. Secondly, this thesis studies the construction of an iterative algorithm for solving the generalized coupled Sylvester matrix equations over generalized bi-symmetric matrices and proves the convergence of the algorithm. Then we obtain the minimum F matrix equations norm solution, and solve the problem of the optimal approximation solution of equations by finding the corresponding new matrix F minimal norm solution of equations. Finally, in the numerical experiments, we find the optimal parameter values of the iterative method for solving the generalized coupled Sylvester matrix equations over generalized bi-symmetric matrices.