矩阵方程X+A~*X^qA=I(0

Perturbation Analysis of the Hermitian Positive Definite Solutions of the Matrix Equation X + A~*X^qA = I(0 < q < 1)

作　　者：李磊[1] 渐令[1] 

机构地区：[1]中国石油大学数学与计算科学学院,东营257061

出　　处：《工程数学学报》2009年第2期297-304,共8页Chinese Journal of Engineering Mathematics

基　　金：石油大学基础研究基金(y080817)

摘　　要：本文利用不动点理论研究了非线性矩阵方程Hermite正定解存在及唯一性条件,并给出了解的存在区间。讨论了方程唯一解的扰动边界,并说明方程是适定的。用数值例子对以上结果作了说明。Based on the fixed-point theory, the conditions for the existence and uniqeness of the Hermitian positive definite solutions to the equation are derived, and the existence domain of solutions is given. A perturbation bound for the unique solution to the nonlinear matrix equation is discussed, and shows that the equation is well-posed. The results are illustrated by numerical examples.

关 键 词：矩阵方程 正定解 扰动边界 

分 类 号：O241.7[理学—计算数学]