摘要
A = （aij） Rn×n is termed bisymmetric matrix if We denote the set of all n×n bisymmetric matrices by BSRn×n Let Where when n =2k, and n = 2k+1, In this paper, we discuss the following two problems: Problem Ⅰ. Given X Rn×m, B Rn×m. Find A S such that Problem Ⅱ. Given A* E Rn×n. Find A SE such that Where is Frobenius norm, and SE is the solution set of Problem I. In this paper the general representation of SE has been given. The necessary and sufficient conditons have been presented for Problem I0. For Problem Ⅱ the expression of the solution has been provided.
A = (aij) R^n×n is termed bisymmetric matrix if We denote the set of all n×n bisymmetric matrices by BSR^(n×n) Let Where when n =2k, and n = 2k+1, In this paper, we discuss the following two problems: Problem Ⅰ. Given X R^n×m, B R^n×m. Find A S such that Problem Ⅱ. Given A* E R^n×n. Find A S_E such that Where is Frobenius norm, and S_E is the solution set of Problem I. In this paper the general representation of S_E has been given. The necessary and sufficient conditons have been presented for Problem I_0. For Problem Ⅱ the expression of the solution has been provided.
出处
《计算数学》
CSCD
北大核心
2000年第2期129-138,共10页
Mathematica Numerica Sinica
基金
国家自然科学基金
关键词
线性流形
双对称阵
逆特征值问题
Bisymmetric matrices, matrix norm, linear manifold, optimal approximation
