TY - JOUR
T1 - On the Nonlinear Matrix Equation $\boldsymbol{X} + \boldsymbol{A}^∗ f_1(\boldsymbol{X})\boldsymbol{A} + \boldsymbol{B}^∗ f_2(\boldsymbol{X}) \boldsymbol{B} = \boldsymbol{Q}$
AU - Sang , Haifeng
AU - Liu , Panpan
AU - Zhang , Shugong
AU - Li , Qingchun
JO - Communications in Mathematical Research 
VL - 3
SP - 280
EP - 288
PY - 2021
DA - 2021/05
SN - 29
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/cmr/19012.html
KW - nonlinear matrix equation, positive definite solution, iterative method.
AB - <p style="text-align: justify;">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 the
existence of solutions for this equation are derived. It is shown that under some
conditions this equation has a unique solution, and an iterative method is proposed
to obtain this unique solution. Finally, a numerical example is given to identify the
efficiency of the results obtained.</p>