The structure-preserving doubling algorithms for positive definite solution to a system of nonlinear matrix equations
Na Huang, Changfeng Ma · Linear and Multilinear Algebra · 2017
In this paper, we consider the positive definite solution to the system of nonlinear matrix equations X+A∗Y-1A=In and Y+B∗X-1B=In, where A,B∈Cn×n are given matrices. We present a structure-preserving doubling algorithm and two modified structure-preserving doubling algorithms to compute the positive definite solution of the system. We prove that the sequences generated by the algorithms converge to the positive definite solution of the system. Finally, some numerical examples are given to show the behaviour of the considered algorithms.