Iterative algorithms for the best approximation to symmetric solutions of the matrix equation AXB=C

Based on the ideas of solving linear equations Mx=f, the Douglas Rachford splitting algorithm, Dykstra´s alternating projection algorithm and LSQR algorithm for solving the optimal approximate symmetric solution of matrix equation AXB=C is given, and the expression of the solution based on LSQR algorithm is obtained. Finally, the iterative time of three algorithms for solving the optimal approximate symmetric solution of matrix equation AXB=C under different matrix sizes is compared by numerical experiments, and the convergence characteristics of the algorithm are analyzed.