Numerical Methods to Solve the Complex Symmetric Stabilizing Solution of the Complex Matrix Equation $X+A^TX^{−1}A=Q$
Yao Yao, Xiaoxia Guo · Journal of Mathematical Study · 2015
When the matrices A and Q have special structure, the structure-preserving algorithmwas used to compute the stabilizing solution of the complexmatrix equation X+ATX−1A=Q. In this paper, we study the numerical methods to solve the complex symmetric stabilizing solution of the general matrix equation X+ATX−1A=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 classifications: 65F10, 65F35, 65F50