一类实对称矩阵的逆特征值问题

The Inverse Eigenvalue Problem of a Kind of Real Symmetric Matrices

研究如下形式实对称矩阵的逆特征值问题An=琢1茁1……茁n-1茁1琢20……0埙……埙0茁n-1……0琢n,An-1=琢1茁1……茁n-2茁1琢20……0埙……埙0茁n-2……0琢n-1茁i>0(i=1,…,n-1)给定(姿,x),(滋,y),其中姿,滋∈R,x∈Rn,y∈Rn-1,茁>0,构造An使得n-1i=1仪茁i=茁,(姿,x),(滋,y)分别是An,An-1,的特征对,并给出相应的算法和数值例子。

In this paper, the inverse eigenvalue problem of a real symmetric matrices as follow：An={（α1β1……βn-1β1…βn-1α2 0 0 0αn）},An-1={（α1β1……βn-2β1…βn-2α2 0 0 0αn-1）}βi〉0（i=1,…,n-1）is studied, where （λ, x） and （μ, y） are given, which are the eigenpairs of ,An An-1, λ,μ∈R,x∈Rn,y∈Rn-1,β〉0.We construct An such that n-1∏i=1βi=β. In the end of the paper a corresponding algorithm and numerical examples are presented.