线性流形上双对称阵逆特征值问题  

THE INVERSE EIGENVALUE PROBLEMS OF BISYMMETRIC MATRICES ON THE LINEAR MANIFOLD

作　　者：张磊 谢冬秀[2] 胡锡炎[3] 

机构地区：[1]湖南省计算所,长沙410012 [2]大连理工大学应用数学系,大连116023 [3]湖南大学应用数学系,长沙410082

出　　处：《计算数学》2000年第2期129-138,共10页Mathematica Numerica Sinica

基　　金：国家自然科学基金

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.

关 键 词：线性流形 双对称阵 逆特征值问题 

分 类 号：O241[理学—计算数学]