由特征值和顺序主子阵构造广义Jacobi矩阵的逆特征值问题

On the generalized Jacobi matrix inverse eigenvalue problem with given eigenvalues and the leading principal submatrix

给定一组复数{λi}2ni=1和一个n×n阶广义Jacobi矩阵,构造了一个2n×2n阶广义Jacobi矩阵,使得其特征值为给定的这组复数,其n×n阶顺序主子阵为给定的广义Jacobi矩阵.得出了问题有解的充分必要条件,给出了一个求解该问题的算法.最后,把该算法应用于数值例子加以说明.

The following problem was discussed ： constructed a 2n×2n generalized Jacobi matrix such that its eigenvalues were the given complex values , λ1,λ2,……,λ2n and its leading n × n principal submatrix was the given generalized Jacobi matrix. A sufficient and necessary condition for the solvability of the problem and an algorithm for solving this problem were obtained, a numerical example was presented to illustrate the algorithm.