线性流形上实对称矩阵最佳逼近  

THE BEST APPROXIMATION BY REAL SYMMETRIC MATRICES ON THE LINEAR MANIFOLD

作　　者：戴华[1] 

机构地区：[1]南京航空航天大学

出　　处：《计算数学》1993年第4期478-488,共11页Mathematica Numerica Sinica

基　　金：国家自然科学基金

摘　　要：1.引言 首先介绍一些记号,IR^(n×m)表示所有n×m实矩阵的全体,SIR^(n×n)表示所有n×n实对称矩阵的全体,OIR^(n×n)表示所有n×n正交矩阵的全体,I_n表示n阶单位矩阵,A^T和A^+分别表示矩阵A的转置和Moore-Penrose广义逆。对A=(a_(ij)),B=(b_(ij))∈IR^(n×m),A＊B表示A与B的Hadamard积,定义为A＊B=(a_(ij)b_(ij))。Let S={A∈SIR^(n×n)|f1(A) =||AX1-B1||= min}, where X_1, B_1 ∈IR^(n×k)_1) SIR^(n×n)= {A∈IR^(n×n)|A^T= A},||.||.is the Frobenius norm. We consider the following problems: Problem Ⅰ. Given X_2, B_2 ∈IR^(n×k)_2, find A ∈ S such that f_2(A) = ||AX_2-B_2||= min. Problem Ⅱ. Given A ∈IR^(n×n), find A∈S_A such that ||A- A||=inf||A-A|| where S_A is the solution set of Problem Ⅰ. The general form of the solution set S_A of Problem Ⅰ is given. The expression of the solution A of Problem Ⅱ is presented. The numerical method is described and numerical experiments are included. Many available results are subsumed under those presented in this paper.

关 键 词：线性流形 实对称矩阵 最佳逼近 

分 类 号：O241.6[理学—计算数学]