Volume 48, Issue 1
Numerical Methods to Solve the Complex Symmetric Stabilizing Solution of the Complex Matrix Equation $X+A^TX^{−1}A=Q$

Yao Yao & Xiao-Xia Guo

J. Math. Study, 48 (2015), pp. 53-65.

Published online: 2015-03

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  • Abstract

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.

  • AMS Subject Headings

65R10, 65N12, 15A24, 65E05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

877133678@qq.com (Yao Yao)

guoxiaoxia@ouc.edu.cn (Xiao-Xia Guo)

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@Article{JMS-48-53, author = {Yao , Yao and Guo , Xiao-Xia}, title = {Numerical Methods to Solve the Complex Symmetric Stabilizing Solution of the Complex Matrix Equation $X+A^TX^{−1}A=Q$}, journal = {Journal of Mathematical Study}, year = {2015}, volume = {48}, number = {1}, pages = {53--65}, abstract = {

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} }
TY - JOUR T1 - Numerical Methods to Solve the Complex Symmetric Stabilizing Solution of the Complex Matrix Equation $X+A^TX^{−1}A=Q$ AU - Yao , Yao AU - Guo , Xiao-Xia JO - Journal of Mathematical Study VL - 1 SP - 53 EP - 65 PY - 2015 DA - 2015/03 SN - 48 DO - http://doi.org/10.4208/jms.v48n1.15.04 UR - https://global-sci.org/intro/article_detail/jms/9909.html KW - Complex matrix, complex symmetric stabilizing solution, fixed-point method, structure preserving algorithm. AB -

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.

Yao , Yao and Guo , Xiao-Xia. (2015). Numerical Methods to Solve the Complex Symmetric Stabilizing Solution of the Complex Matrix Equation $X+A^TX^{−1}A=Q$. Journal of Mathematical Study. 48 (1). 53-65. doi:10.4208/jms.v48n1.15.04
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