摘要
令S={A∈ASn｜AZ=Y,ZT1ZT+1YT2=YT2,Y1Z+2Z2=Y1,ZT1Y1=-YT2Z2,Y,Z∈Rn×m},这里(ZT1 ZT2)=ZTD,(YT1 YT2)=YTD.研究了如下问题:问题Ⅰ 已知X,B∈Rn×n,找A∈S使‖AX-B‖=min.问题Ⅱ 给定A ∈Rn×n,找^A∈SE使‖A -^A‖=min A∈SE‖A -A‖.这里SE是问题Ⅰ的解集合,给出问题Ⅰ的解集合表达式和问题Ⅱ的逼近解.
Let S = { A ∈ ASn | AZ = Y, Z1TZ 1T+ Y2T = Y2T, Y1 Z2+ Z2 = Y1, Z 1T Y1 = - Y2T Z 2, Y, Z ∈ Rn×m}, where ( Z1 T Z2T) = ZTD, (Y1 T Y2T) = YTD, discussed the following two problems: Problem I. Given X, B ∈ Rn×n, find A∈S such that || AX - B || = min. Problem II. Given A * ∈ Rn×n, find Aˆ ∈ SE such that || A* - Aˆ || = min∀A∈SE || A* - A ||, where S E is the solution set of Problem I. The general representation of SE has been given, for Problem II the expression of the solution has been provided.
出处
《晓庄学院自然科学学报》
EI
CAS
北大核心
2005年第2期11-14,共4页
Journal of Natural Science of Hunan Normal University
基金
湖南省教育厅资助项目(04C514)
