An Extended Hamiltonian Algorithm for the Numerical Solution of the Nonlinear Matrix Equation

In this paper, a second-order learning algorithm was used to solve a class of the nonlinear matrix equations. Specifically, the extended Hamiltonian algorithm was proposed based on manifold of positive definite symmetric matrices. Furthermore, this algorithm was compared with the multi-step iterative method to analyze its operation character. Finally, the simulation results show that, the convergence speed of the extended Hamiltonian algorithm is faster than the traditional algorithm.