New matrix iterative methods for constraint solutions of the matrix equation

In this paper, two new matrix iterative methods are presented to solve the matrix equation A X B = C , the minimum residual problem min X ∈ S ‖ A X B − C ‖ and the matrix nearness problem min X ∈ S E ‖ X − X ∗ ‖ , where S is the set of constraint matrices, such as symmetric, symmetric R -symmetric and ( R , S ) -symmetric, and S E is the solution set of above matrix equation or minimum residual problem. These matrix iterative methods have faster convergence rate and higher accuracy than the matrix iterative methods proposed in Deng et al. (2006) [13], Huang et al. (2008) [15], Peng (2005) [16] and Lei and Liao (2007) [17]. Paige’s algorithms are used as the frame method for deriving these matrix iterative methods. Numerical examples are used to illustrate the efficiency of these new methods.