非线性矩阵方程Xm-A∗X-s A-B∗X-t B=Q的Hermitian正定解

摘要

研究了非线性矩阵方程Xm-A∗X-s A-B∗X-t B=Q的Hermitian正定解,其中Q为Hermitian正定矩阵,m∈[1,+¥)且s,t∈(0,1]。给出了该矩阵方程Hermitian正定解存在的充分必要条件,同时也分析了求解其Hermitian正定解的迭代算法的收敛性。实验结果表明了该迭代算法的有效性。%In this paper,the Hermitian positive definite solutions of the nonlinear matrix equation Xm-A∗X-sA-B∗X-tB=Q are studied,where Q is a Hermitian positive definite matrix,m∈[1,+¥) and s,t∈(0,1]. The necessary and sufficient conditions for the existence of the Hermitian positive definite solutions are derived and the convergence of the proposed iteration method is analyzed. Numerical results demonstrate the efficiency of the proposed iteration method.