Two structure-preserving-doubling like algorithms for obtaining the positive definite solution to a class of nonlinear matrix equation

In this paper, we present two structure-preserving-doubling like algorithms for obtaining the positive definite solution of the nonlinear matrix equation X+AHX¯−1A=Q, where X∈Cn×nX∈Cn×n is an unknown matrix and Q∈Cn×nQ∈Cn×n is a Hermitian positive definite matrix. We prove that the sequences generated by the algorithms converge to the positive definite solution of the considered matrix equation R-quadratically. In addition, we also present some numerical results to illustrate the behavior of the considered algorithm.