Two iterative algorithms to compute the bisymmetric solution of the matrix equation

In this paper, two matrix iterative methods are presented to solve the matrix equation A1X1B1 + A2X2B2 + ... + AlXlBl = C the minimum residual problem ‖ ∑l i=1 AiX̂iBi− C‖F = minXi∈BRni×ni‖ ∑l i=1 AiXiBi−C‖F and the matrix nearness problem [X̂1, X̂2, ..., X̂l] = min[X1,X2,...,Xl]∈SE ‖[X1, X2, ..., Xl] − [X̃1, X̃2, ..., X̃l]‖F , where BRni×ni is the set of bisymmetric matrices, and SE is the solution set of above matrix equation or minimum residual problem. These matrix iterative methods have faster convergence rate and higher accuracy than former methods. Paige’s algorithms are used as the frame method for deriving these matrix iterative methods. The numerical example is used to illustrate the efficiency of these new methods. Keywords—Bisymmetric matrices, Paige’s algorithms , Least square.