Numerical Methods to Solve the Complex Symmetric Stabilizing Solution of the Complex Matrix Equation $X+A^TX^{−1}A=Q$
Year: 2015
Author: Yao Yao, Xiao-Xia Guo
Journal of Mathematical Study, Vol. 48 (2015), Iss. 1 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v48n1.15.04
Journal of Mathematical Study, Vol. 48 (2015), Iss. 1 : pp. 53–65
Published online: 2015-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
Keywords: Complex matrix complex symmetric stabilizing solution fixed-point method structure preserving algorithm.