Hermitian Positive Definite Solutions of the Matrix Equation X + A~*X~(-q)A=Q(q≥1)
Liao An · Journal of Mathematical Research and Exposition · 2009
In this paper,Hermitian positive definite solutions of the nonlinear matrix equation X + A*X-qA = Q(q ≥ 1) are studied.Some new necessary and sufficient conditions for the existence of solutions are obtained.Two iterative methods are presented to compute the smallest and the quasi largest positive definite solutions,and the convergence analysis is also given.The theoretical results are illustrated by numerical examples.