@article{Li2025, 
author = {Changzhou Li and Boyu Wang and Chao Yuan and Shiliang Chen},
title = {On a parameterized inversion-free iterative algorithm for solving the nonlinear matrix equation    X  +      ∑          i      =      1              m            A          i              ∗            X          −              p                  i                          A          i        =  I},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {8},
pages = {19018-19032},
keywords = {nonlinear matrix equations, positive definite solution, inversion-free iteration methods, convergence analysis},
url = {https://www.sciopen.com/article/10.3934/math.2025850},
doi = {10.3934/math.2025850},
abstract = {In this paper, we propose a parameterized inversion-free iterative algorithm to compute the positive definite solution of the nonlinear matrix equation    X  +      ∑          i      =      1              m            A          i              ∗            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.}
}