Fixed-point accelerated iterative method to solve nonlinear matrix equation X-∑i=1mAi∗X-1Ai=Q∗

Nonlinear matrix equation X-∑i=1mAi∗X-1Ai=Qhas wide applications in control theory, dynamic planning, interpolation theory and random filtering. In this paper, a fixed-point accelerated iteration method is proposed, and based on the basic characteristics of the Thompson distance, the convergence and error estimation of the proposed algorithm are proved. Numerical comparison experiments show that the proposed algorithm is feasible and effective.