对称箭形矩阵最大最小特征对的逆特征值问题的一个有效算法

An Efficient Algorithm for Solving Inverse Max-min Eigenvalue Problem of Symmetric Arrow-head Matrices

研究一个对称箭形矩阵的逆特征值问题:给定非零向量x∈Rn,y∈Rk,k≤n,以及两个实数λ>μ,求对称箭形矩阵A,使得(,λx)是对称箭形矩阵A的最大特征对,而(μ,y)是A的k阶顺序主子阵Ak的最小特征对。给出该问题有解的充分必要条件,并且给出一个算法计算该问题的一个解,数值实例说明是可行的。

An inverse eigenvalue problem of symmetric arrow-head matrices is considered in the paper： for given non- zeros x∈ R^n, y ∈ R^k, k ≤ n, and two different real numbers λ 〉μ, find a symmetric arrow-head matrix A such that （ λ, x ）is the maximal eigenpair of A and （μ, y） is the minimal eigenpair of k leading principal subniatrix of A. The necessary and sufficient conditions for solvability has been given in the paper, and an algorithm has been presented to compute a solution. A numerical example shows that the algorithm is feasible and efficient.