Hermite Positive Definite Solution of a Class of Matrix Equation

AbstractIn this paper, the Hermite positive definite solutions of the nonlinear matrix equation XS+A*X−tA=Q are discussed. A sufficient condition and two necessary and sufficient conditions for the existence of Hermite positive definite solutions for this equation are derived. The existence of minimal Hermite positive definite solution is also studied here, and an iterative method for obtaining the minimal Hermite positive definite solution is given