一个非线性矩阵方程的迭代解法  

An Iterative Method of Solving a Nonlinear Matrix Equation

作　　者：熊慧军[1] 

机构地区：[1]长沙大学数学与信息科学系,中国长沙410003

出　　处：《湖南师范大学自然科学学报》2006年第4期6-8,共3页Journal of Natural Science of Hunan Normal University

基　　金：湖南省自然科学基金资助项目(03JJY6028)

摘　　要：构造了一个求解非线性矩阵方程X+A*X-nA=I的正定解的迭代公式,这里A为非奇异正规阵.在给定条件下,证明了该迭代法的收敛性,并给出了误差估计式.An iterafive method which is used to find the positive definite solution of the nonlinear matrix equation X ＋ A^＊ X^-n A = I is constructed, where the matrix A is nonsingular and A^＊A = AA^＊ . The convergence of the iterative method is proved under some conditions, and an error estimate formula is presented.

关 键 词：非线性矩阵方程 正定解 迭代法 

分 类 号：O241.1[理学—计算数学]