The parameterized accelerated iteration method for solving the matrix equation AXB=C.

By introducing two parameters in the splittings of the matrices A and B, this paper presents a parameterized accelerated iteration (PAI) method for solving the matrix equation A X B = C . The convergence property of the PAI method and the choices of the parameters are thoroughly investigated. Additionally, based on some special splittings of the matrices A and B, several variants of the PAI method are established. Furthermore, for some certain cases, the optimal parameters can be determined, and it is demonstrated that the PAI method is more efficient than the gradient-based iteration (GBI) method (Ding et al. Appl. Math. Comput. 197, 41–50 2008). Finally, by comparing it with several existing iteration methods, the effectiveness of the PAI method is verified through four numerical examples. [ABSTRACT FROM AUTHOR]