Abstract
In this paper, based on the iteration framework [10], by introducing two tuning parameters α,β in the splittings of the matrices A and B, a parameterized two-step iteration (PTSI) method is presented for solving the matrix equation AXB=C. In the sequel, the convergence property and choices of the parameters α,β are analyzed in detail. For some special cases of the matrices A and B, the corresponding PTSI methods are also investigated, and the optimal parameters α,β can be obtained for the symmetric positive definite (SPD) matrices A and B. In addition, some comparison results of the PTSI method are given for the M-matrices A,B compared with the TSI method [10]. Finally, several numerical examples are performed to verify the efficiencies of the PTSI method and choices of the optimal parameters.
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