On a parameterized inversion-free iterative algorithm for solving the nonlinear matrix equation $X+\sum _{i=1}^m{A}_i^{\ast }{X}^{-p_i}{A}_i=I$

In this paper, we propose a parameterized inversion-free iterative algorithm to compute the positive definite solution of the nonlinear matrix equation $X+\sum _{i=1}^m{A}_i^{\ast }{X}^{-p_i}{A}_i=I$. Then, we prove that the proposed algorithm converges. Finally, in comparison with three well-known existing algorithms, the accuracy and effectiveness of the proposed algorithm are demonstrated by some numerical examples.