摘要
研究了矩阵方程广义自反矩阵解及其最佳逼近解。首先,在充分研究该类矩阵性质的基础上,将约束矩阵方程化为等价的无约束问题,并建立了两者解之间的关系。其次,给出问题有解的充要条件及解集合的通式。最后给出了最佳解的表达式。
Generalized reflexive solutions of the matrix equation and their optimal approximation were discussed.Firstly,based on the full study of the properties of this class of matrices,the constrained matrix equation was reformulated into an equivalent unconstrained problem and the relation between the solutions of the two classes of problems was established.Secondly,the necessary and sufficient conditions for the solvability of the problem and the general form of the solution set were proposed.Finally,the expression of the optimal approximation solution was given.
出处
《武汉理工大学学报（信息与管理工程版）》
CAS
2012年第1期56-59,共4页
Journal of Wuhan University of Technology：Information & Management Engineering
基金
国家自然科学基金资助项目(60872129)
关键词
广义自反矩阵
最佳逼近
F-范数
generalized reflexive matrix
optimal approximation
frobenius norm
