Hermitian Positive Definite Solution of the Matrix Equation X=Q+∑i=1mAi(B+X-1)-1Ai*. (24th September 2014) - Li, Chun-Mei; Peng, Jing-Jing
Abstract : We consider the Hermitian positive definite solution of the nonlinear matrix equation X = Q + ∑ i = 1 m A i ( B + X - 1 ) - 1 A i * . Some new sufficient conditions and necessary conditions for the existence of Hermitian positive definite solutions are derived. An iterative method is proposed to compute the Hermitian positive definite solution. In the end, an example is used to illustrate the correctness and application of our results.