Positive Definite Solutions of the Matrix Equation X-A*X~(-α)A-B*X~(-β)B=I
DU Zhong-fu · Journal of Jilin University(Science Edition) · 2010
The positive definite solutions of the matrix equation X-A*X-αA-B*X-βB=I,α,β∈(0,1] were investigated.Necessary and sufficient conditions for the existence of positive definite solutions were derived,which generalize the existing related results.A necessary 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.