Perturbation Analysis of the Hermitian Positive Definite Solutions of the Matrix Equation X + A~*X~qA = I(0 < q < 1)
Ling Jian · Gongcheng shuxue xuebao · 2009
Based on the fixed-point theory, the conditions for the existence and uniqeness of the Hermitian positive definite solutions to the equation are derived, and the existence domain of solutions is given. A perturbation bound for the unique solution to the nonlinear matrix equation is discussed, and shows that the equation is well-posed. The results are illustrated by numerical examples.