The Open Applied Informatics Journal

2009, 3 : 22-33
Published online 2009 August 20. DOI: 10.2174/1874136300903010022
Publisher ID: TOAINFOJ-3-22

Riccati Equation Solution Method for the Computation of the Solutions of X + AXA = Q and X - AXA = Q

Maria Adam , Nicholas Assimakis , Grigoris Tziallas and Francesca Sanida
Department of Computer Science and Biomedical Informatics, University of Central Greece, Lamia 35100, Greece.

ABSTRACT

A test is developed for checking the existence of a finite number of solutions of the matrix equations X + ATX-1 = Q and X - ATX-1A = Q when A is a nonsingular matrix. An algebraic method for computing all the solutions of these matrix equations is proposed. The method is based on the algebraic solution of the corresponding discrete time Riccati equations. The number of solutions is also derived. The extreme solutions are computed as well

Keywords:

Matrix theory, matrix equations, eigenvalue-eigenvector, Riccati equation.