Abstract:

The positive definite solutions of the matrix equation X-A*X^-αA-B*X^-βB=Iα,β∈(0,1］ were investigated. Necessary and sufficient conditions for   the existence of positive definite solutions were derived, which generalize the existing related results. Anecessary condition for the existence of the equation to have only a solution and the iterative formula for this solution were obtained. Finally, we got an inverse iterative method for solving the equation.

Key words: matrix equation, positive definite solution, iterative method