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 + A(H)(X) over bar (-1) A = Q, where X is an element of C-nxn is an unknown matrix and Q is an element of C-nxn 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. (C) 2015 Elsevier Ltd. All rights reserved.