矩阵方程(A￣TXA,B￣TXB)=(C,D)的对称半正定解  

Symmetric Positive Semidefinite Solutions of the Matrix Equation (ATXA,BTXB)=(C,D)

作　　者：廖安平[1] 

机构地区：[1]湖南师范大学计算机科学系

出　　处：《湖南师范大学自然科学学报》1997年第4期10-13,29,共5页Journal of Natural Science of Hunan Normal University

基　　金：国家自然科学基金

摘　　要：讨论了矩阵方程（ＡＴＸＡ，ＢＴＸＢ）＝（Ｃ，Ｄ）的对称半正定解．利用广义奇异值分解导出了该矩阵方程有对称半正定解的充分必要条件。The symmetric positive semidefinite solutions of the matrix equation (ATXA,BTXB)=(C,D) is considered in this paper. Necessary and sufficient conditions for the matrix equation to have symmetric positive semidefinite solutions are derived using the generalized singularvalue decomposition. The expression for the general symmetric positive semidefinite solution is given when certain conditions hold.

关 键 词：数值代数 对称半正定解 矩阵方程 奇异值 

分 类 号：O151.21[理学—数学] O241.6[理学—基础数学]