Abstract.

We explore a system of nonlinear matrix equations. We correct Ali and Hossein’s calculations [On the positive definite solution of a class of pair of nonlinear matrix equations, Computational and Applied Mathematics, 39(2): 102(2020), 1-30.] and address specific con ditions for the existence of a positive definite solution. The convergence analysis and rate of convergence of a new approach for obtaining the maximal positive definite solution are then discussed. We provide enough examples to show the new iteration strategy’s efficacy and the convergence analysis of nonlinear matrix equations.

Keywords:

nonlinear matrix equation, positive definite solutions, iterative methods.