摘要
R^(n×m)表示所有n×m阶实阵集合,R_r^(n×m)表示R^(n×m)中秩为r的子集.R_K表示所有K阶对称非负定阵集合.A≥0(>0)表示方阵A对称非负定(正定).R(A),N(A),A^+分别表示A的列空间,零空间和Moore-Penrose广义逆.dim(·)表示子空间维数,I_K表示K阶单位阵.||·||表示Frobenius范数.现考虑如下问题:
This paper, considers the following two problems: Problem Ⅰ. Given X, B R^(n×m),find A∈P_u such that AX = B,where P_u = {A∈R^(n×m)|A=A^x, x^TAx≥0,?x∈R^u}. Problem Ⅱ. Given A∈R^n×n, find A∈S_E such that‖A-A‖ - inf‖A - A‖,where ‖·‖ is Frobenius norm, and S_E denotes the solution set of problem Ⅰ. The necessary and sufficient condition, under which S_E is nonempty, is studied.The general form of S_E is given. For problem Ⅱ, the expression of the solution isprovided.
出处
《计算数学》
CSCD
北大核心
1989年第4期337-343,共7页
Mathematica Numerica Sinica
