The positive definite solution to a nonlinear matrix equation
Jie Meng, Hyun‐Min Kim · Linear and Multilinear Algebra · 2015
In this paper, we consider a nonlinear matrix equation, which has the form , where is a positive integer, is an arbitrary complex matrix and is an Hermitian positive definite matrix. A double of elegant estimates of the Hermitian positive definite solution are obtained. Three iterative methods for computing the Hermitian positive definite solution are proposed. Some numerical examples to show the efficiency of the proposed iterative methods are provided.