On the Positive Definite Solutions of a Nonlinear Matrix Equation

[摘要] The positive definite solutions of the nonlinearmatrix equationXs+A∗f(X)A=Qare discussed. A necessary and sufficient condition for the existence of positive definite solutions for this equation is derived. Then, the uniqueness of the Hermitian positive definite solution is studied based on an iterative method proposed in this paper. Lastly the perturbation analysisfor this equation is discussed.

[学科分类] 应用数学