On the Positive Definite Solutions of Nonlinear Matrix Equation Year: 2014 Volume: 8 Issue: 3 586 - 588 Pages Authors: Tian Baoguang Liang Chunyan Chen Nan Abstract: In this paper, the nonlinear matrix equation is investigated. Based on the fixed-point theory, the boundary and the existence of the solution with the case r>-δi are discussed. An algorithm that avoids matrix inversion with the case -1 Keywords: Nonlinear matrix equation Positive definite solution The maximal-minimal solution Iterative method Free-inversion