The inversion-free iterative methods for a system of nonlinear matrix equations
Na Huang, Changfeng Ma, Jia Tang · International Journal of Computer Mathematics · 2015
In this paper, we consider the positive-definite solution to a system of nonlinear matrix equations, X1+A∗X2−α1A=I and X2+B∗X1−α2B=I, where α1,α2 are two positive constants and A,B∈Cr×r are given matrices. We proposed two inversion-free iterative algorithms for obtaining the maximal positive-definite solution of the system. And we prove that the sequences generated by the iterative schemes are monotonically increasing and bounded above. Finally, some numerical examples are given to show the behaviour of the considered algorithms.