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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 ¯ − 1 A = Q , where X ∈ C n × n is an unknown matrix and Q ∈ C n × 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. [ABSTRACT FROM AUTHOR]