On the Nonlinear Matrix Equation $\boldsymbol{X} + \boldsymbol{A}^∗ f_1(\boldsymbol{X})\boldsymbol{A} + \boldsymbol{B}^∗ f_2(\boldsymbol{X}) \boldsymbol{B} = \boldsymbol{Q}$ (Communications in Mathematical Research, 2021)
In this paper, nonlinear matrix equations of the form $\boldsymbol{X} + \boldsymbol{A}^∗ f_1(\boldsymbol{X})\boldsymbol{A} + \boldsymbol{B}^∗ f_2(\boldsymbol{X}) \boldsymbol{B} = \boldsymbol{Q}$ are discussed. Some necessary and sufficient conditions for theexistence of solutions for this equation are derived. It is shown that under someconditions this equation has a unique solution, and an iterative method is proposedto obtain this unique solution. Finally, a numerical example is given to identify theefficiency of the results obtained.
Keywords: nonlinear matrix equation; positive definite solution; iterative method.