Newton’s method for solving a class of nonlinear matrix equations

摘要

In this paper, a class of nonlinear matrix equations X=Q+AH(I⊗X−C)−1A is considered. An equivalent form of this equation is derived, and the properties of the solutions are studied. Then Newton’s iterative method is applied to solve this equivalent one. Finally, two numerical examples are given to illustrate the efficiency of Newton’s method.