| 一类约束矩阵方程的可解条件与最佳逼近问题 |
| |
| 引用本文： | 王学锋,张忠志.一类约束矩阵方程的可解条件与最佳逼近问题[J].安徽大学学报(自然科学版),2011,35(4). |
| |
| 作者姓名： | 王学锋 张忠志 |
| |
| 作者单位： | 东莞理工学院数学系,广东东莞,523808 |
| |
| 基金项目： | 国家自然科学基金资助项目 |
| |
| 摘 要： | 利用空间分解理论和矩阵的奇异值分解等方法,证明了矩阵方程AX+B Y=Z在矩阵集合Cnr×n(P,Q)×Cna×n(P,Q)中可解的充分必要条件,并得到通解的表达式.对于相关逼近问题,证明最佳逼近解的存在唯一性,得到解的显式表达式.最后,给出最佳逼近解的扰动分析.
|
| 关 键 词： | 广义自反矩阵 广义反自反矩阵 约束矩阵方程 最佳逼近 |
The solvability conditions for a kind of constrained matrix equation and relevant optimal approximate problem |
| |
| WANG Xue-feng,ZHANG Zhong-zhi.The solvability conditions for a kind of constrained matrix equation and relevant optimal approximate problem[J].Journal of Anhui University(Natural Sciences),2011,35(4). |
| |
| Authors: | WANG Xue-feng ZHANG Zhong-zhi |
| |
| Abstract: | By use of the decomposition theory of a space and the singular value decomposition of a matrix,some necessary and sufficient conditions for the solvability of the matrix equation AX+BY=Z in matrix set Cn×nr(P,Q)×Cn×na(P,Q) are provided,the general representation of the solutions is derived for a solvable case.The expression of the solution for the corresponding optimal approximation problem is given and a perturbation of the solution(A~,B~) is analyzed. |
| |
| Keywords: | generalized reflexive matrix generalized anti-reflexive matrix constrained matrix equation optimal approximation |
| 本文献已被 万方数据 等数据库收录！ |
|
