An accelerated technique for solving the positive definite solutions of a class of nonlinear matrix equations

Nonlinear matrix equations (NMEs) are encountered in many applications of control and engineering problems. In this work, we establish a complete study for a class of nonlinear matrix equations. With the aid of Sherman Morrison Woodbury formula, we have shown that any equation in this class has the maximal positive definite solution under certain conditions. Furthermore, a thorough study of properties about this class of matrix equations is provided. An acceleration of iterative method with R-superlinear convergence is then designed to solve the maximal positive definite solution. Two numerical experiments demonstrate that our methods perform efficiently and reliably.