ON HERMITIAN POSITIVE DEFINITE SOLUTIONS OF MATRIX EQUATION X-A^＊X^-2 A=I  

作　　者：Yu-hai Zhang 

机构地区：[1]School of Mathematics and System Sciences, Shandong University, Jinan 250100, China

出　　处：《Journal of Computational Mathematics》2005年第4期408-418,共11页计算数学（英文）

摘　　要：The Hermitian positive definite solutions of the matrix equation X-A^＊X^-2 A=I are studied. A theorem for existence of solutions is given for every complex matrix A. A solution in case A is normal is given. The basic fixed point iterations for the equation are discussed in detail. Some convergence conditions of the basic fixed point iterations to approximate the solutions to the equation are given.The Hermitian positive definite solutions of the matrix equation X-A^＊X^-2 A=I are studied. A theorem for existence of solutions is given for every complex matrix A. A solution in case A is normal is given. The basic fixed point iterations for the equation are discussed in detail. Some convergence conditions of the basic fixed point iterations to approximate the solutions to the equation are given.

关 键 词：Matrix equation Positive definite solution Iterative methods 

分 类 号：O15[理学—数学]