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Volume 29, Issue 3
On the Nonlinear Matrix Equation $\boldsymbol{X} + \boldsymbol{A}^∗ f_1(\boldsymbol{X})\boldsymbol{A} + \boldsymbol{B}^∗ f_2(\boldsymbol{X}) \boldsymbol{B} = \boldsymbol{Q}$

Haifeng Sang, Panpan Liu, Shugong Zhang & Qingchun Li

Commun. Math. Res., 29 (2013), pp. 280-288.

Published online: 2021-05

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  • Abstract

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.

  • Keywords

nonlinear matrix equation, positive definite solution, iterative method.

  • AMS Subject Headings

15A24

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-29-280, author = {Sang , HaifengLiu , PanpanZhang , Shugong and Li , Qingchun}, title = {On the Nonlinear Matrix Equation $\boldsymbol{X} + \boldsymbol{A}^∗ f_1(\boldsymbol{X})\boldsymbol{A} + \boldsymbol{B}^∗ f_2(\boldsymbol{X}) \boldsymbol{B} = \boldsymbol{Q}$}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {29}, number = {3}, pages = {280--288}, abstract = {

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.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19012.html} }
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 -

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.

Sang , HaifengLiu , PanpanZhang , Shugong and Li , Qingchun. (2021). 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 . 29 (3). 280-288. doi:
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