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矩阵方程X=Q-A^*（I_mX—C）^-1A的正定解

Positive Definite Solutions of the Matrix Equation X=Q-A^*（I_mX-C）^-1A

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【Author】 YAO Guo-zhu~1 LIAO An-ping~(2,3) DUAN Xue-feng~4 (1- College of Mathematics and Computing Science,Changsha University of Science and Technology, Changsha 410114;2- College of Mathematics and Econometrics,Hunan University,Changsha 410082; 3- Institute of Mathematics,Changsha University,Changsha 410003;4- School of Mathematics and Computational Science,Guilin University of Electronic Technology,Guilin 541004)

【机构】长沙理工大学数学与计算科学学院；湖南大学数学与计量经济学院；长沙学院数学研究所；桂林电子科技大学数学与计算科学学院；

【摘要】本文利用Kronecker积的性质,得到了非线性矩阵方程X=Q-A^*（I_m（?）X-C）^-1A存在正定解的充分必要条件。运用有界序列的收敛原理,给出了求解方程的不动点迭代与无逆迭代两种迭代方法。数值例子验证了这两种迭代方法是行之有效的。更多还原

【Abstract】 The nonlinear matrix equation X = Q - A*（I_m（?）X - C）^-1 A is considered in this paper. A sufficient and necessary condition for the existence of positive definite solutions to this equation is presented by using properties of the Kronecker product.Two iterative methods for solving the equation are constructed by making use of the principle for the bounded sequence.The feasibility and effectiveness of the iterative methods are verified by a numerical example.更多还原