On The Solutions Of Two Nonlinear Matrix Equations

In this paper,we discuss two matrix equations X-A^*X^-1A+B^*X^-tB=I_n and X+A^*X^-1A+B^*X^-tB=I_n. We design iterative methods for obtaining positive definite solutions of these equations.Sufficent and necessary conditions for the existence of a positive definite solution of X-A^*X^-1A+B^*X^-tB=I_n,whent=2.Design two iterative methods for obtaining solutions of equation X+A^*X^-1A+B^*X^-tB=I_n ,when t=2 and 0