线性流形上的逆特征值问题  

THE INVERSE EIGENVALUE PROBLEMS ON THE LINEAR MANIFOLD

作　　者：戴华[1] 

机构地区：[1]南京航空航天大学理学院,210016

出　　处：《高等学校计算数学学报》1995年第4期357-366,共10页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金

摘　　要：1 问题的提法先说明一些记号,R^(n×m)表示所有n×m实矩阵的全体。OR^(n×m)Letwhere X1,Z1∈n×k1,Y1,W1∈Rn×l1. We consider the following problems. Problem Ⅰ Given Z2,X2∈Rn×k2,Y2,W2∈nxl2,find A∈S such thatf(A) = ‖ AXx - Z2‖ 2 + ‖ YΥ2A - WΥ2‖ 2 =min, where ‖·‖ is the Frobenius norm.Problem Ⅱ Given A∈Rn×n,find A∈SA such that‖A - A‖ = inf ‖ A - A ‖, V A∈SAwhere SA is the solution set of Problem Ⅰ.The general form of the solution set SA of Problem 111 is given. The expression of the solution A to problem Ⅱ is Presented. A numerical method for solving problem Ⅰ and Ⅱ is described. These results are applied to a class of inverse eigenvalue problems. Two numerical examples are given.

关 键 词：线性流形 逆特征值问题 矩阵 

分 类 号：O241.6[理学—计算数学]