On matrix equations X±A*X−2A=I Original Research Article

The two matrix equations X+A*X−2A=I and X−A*X−2A=I are studied. We construct iterative methods for obtaining positive definite solutions of these equations. Sufficient conditions for the existence of two different solutions of the equation X+A*X−2A=I are derived. Sufficient conditions for the existence of positive definite solutions of the equation X−A*X−2A=I are given. Numerical experiments are discussed.