| 一类约束矩阵方程的可解条件与最佳逼近问题 |
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| 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) |
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| 作者姓名： | 王学锋 张忠志 |
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| 作者单位： | 东莞理工学院数学系,广东东莞,523808 |
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| 基金项目： | 国家自然科学基金资助项目 |
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| 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.
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| 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 |
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| 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) |
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| Authors: | WANG Xue-feng ZHANG Zhong-zhi |
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| 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. |
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| Keywords: | generalized reflexive matrix generalized anti-reflexive matrix constrained matrix equation optimal approximation |
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