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When the matrices $A$ and $Q$ have special structure, the structure-preserving algorithm was used to compute the stabilizing solution of the complex matrix equation $X+A^TX^{-1}A=Q.$ In this paper, we study the numerical methods to solve the complex symmetric stabilizing solution of the general matrix equation $X+A^TX^{-1}A=Q.$ We not only establish the global convergence for the methods under an assumption, but also show the feasibility and effectiveness of them by numerical experiments.
}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v48n1.15.04}, url = {http://global-sci.org/intro/article_detail/jms/9909.html} }When the matrices $A$ and $Q$ have special structure, the structure-preserving algorithm was used to compute the stabilizing solution of the complex matrix equation $X+A^TX^{-1}A=Q.$ In this paper, we study the numerical methods to solve the complex symmetric stabilizing solution of the general matrix equation $X+A^TX^{-1}A=Q.$ We not only establish the global convergence for the methods under an assumption, but also show the feasibility and effectiveness of them by numerical experiments.