Abstract
In this paper, we consider the positive-definite solution to a system of nonlinear matrix equations, and
, where
are two positive constants and
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.
Disclosure statement
No potential conflict of interest was reported by the authors.