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2010•Unpublished venueRequires access

ON THE EXISTENCE AND PROPERTIES OF THE POSITIVE DEFINITE SOLUTION OF THE MATRIX EQUATION

N. H. Sweilam, M. M. Khader

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Abstract

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.

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What this paper is about

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.

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Available abstract

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.

Key concepts: Positive-definite matrix, Mathematics, Matrix (chemical analysis), Applied mathematics, Nonlinear system, Mathematical analysis, Mathematical optimization, Physics

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