矩阵方程X+A~*X^qA=I(q>0)的Hermite正定解  

The Hermitian positive definite solutions of the matrix equation X+A~*X^qA=I(q>0)

作　　者：李磊[1] 张玉海[1] 

机构地区：[1]山东大学数学与系统科学学院,山东济南250100

出　　处：《山东大学学报（理学版）》2006年第4期32-39,共8页Journal of Shandong University(Natural Science)

基　　金：数学天元基金资助项目(A0324654)

摘　　要：考虑非线性矩阵方程X+A*XqA=I(q>0),其中I是n×n阶的单位矩阵,A是n×n阶的复矩阵.推导出矩阵方程Hermite正定解的性质及方程迭代求解,并给出解的惟一性的显式表达式.以上结果用数值例子来说明.Consider the nonlinear matrix equation X ＋ A^＊ X^qA = I with q 〉 0, where I is the n x n identity matrix, A is the n x n complex matrix. Some properties of the solution and the basic fixed point iterations for the equation are discussed in some detail, and the explicit formulations about uniqueness of the solution are given. The results are illustratd by numerical examples.

关 键 词：矩阵方程 正定解 迭代方法 

分 类 号：O241.7[理学—计算数学]