Numerical Methods to Solve the Complex Symmetric Stabilizing Solution of the Complex Matrix Equation $X+A^TX^{−1}A=Q$ (Journal of Mathematical Study, 2018)
When the matrices $A$ and $Q$ have special structure, the structure-preservingalgorithm 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 complexsymmetric stabilizing solution of the general matrix equation $X+A^TX^{-1}A=Q.$ Wenot only establish the global convergence for the methods under an assumption, butalso show the feasibility and effectiveness of them by numerical experiments.
Keywords: Complex matrix; complex symmetric stabilizing solution; fixed-point method; structure preserving algorithm.