Weighted Average Iterative Algorithm for Solving a Nonlinear Matrix Equation

Nonlinear matrix equation X^p - ^m∑_i=1A^T_iX^-1A_i=Q has extensive applications in control theory, ladder networks, dynamic programming and stochastic filtering. In this paper, we propose a weighted average iterative algorithm to solve this nonlinear matrix equation. Based on the basic characteristics of the Thompson metric space, the convergence and error estimation formula of the algorithm are proved. Numerical experiments to illustrate the feasibility and effectiveness of the proposed algorithm are given.