An efficient inversion-free method for solving the nonlinear matrix equation Xp+∑j=1mAj*X−qjAj=Q. Issue 7 (May 2022) - Erfanifar, Raziyeh; Sayevand, Khosro; Hajarian, Masoud
Abstract: In this article, we first introduce the necessary and sufficient conditions for the existence of the solution of nonlinear matrix equation X p + ∑ j = 1 m A j * X − q j A j = Q . Then we propose the inversion-free iteration method to find this solution of the nonlinear matrix equation. Finally, the accuracy and effectiveness of the proposed method in compare to some existing algorithms are demonstrated by various numerical examples.