【摘要】 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。更多还原

【Abstract】 An inverse eigenvalue problem of symmetric arrow-head matrices is considered in the paper: for given non-zeros x∈Rn,y∈Rk,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 submatrix 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.更多还原