ON THE EXISTENCE AND PROPERTIES OF THE POSITIVE DEFINITE SOLUTION OF THE MATRIX EQUATION
Nasser Hassan Sweilam, M. M. Khader · 2010
The main goal of this paper is to discuss the matrix equation X = I + A � p X 1 A. This type of the nonlinear matrix equations has many applications, such as in the analysis of ladder networks, optimal control theory, dynamic pro- gramming. An iterative method to find a positive definite solution is introduced. Special attention for necessary and sufficient conditions ofthe existence of a positive definite solution of the problem is implemented. Numerical examples are given to ensure the efficiency of the proposed method.