由部分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 partial given eigenvalues and the leading principal submatrix

作　　者：潘云兰[1] 秦立[1] PAN yunlan;Qin(College of Machematics,Physics and Information Engineering,Zhejiang Normal Universty,Jihua 321004,China)

机构地区：[1]浙江师范大学数理与信息工程学院,浙江金华321004

出　　处：《浙江师范大学学报（自然科学版）》2018年第2期130-137,共8页Journal of Zhejiang Normal University:Natural Sciences

基　　金：国家自然科学基金资助项目(11671365);浙江省自然科学基金资助项目(17A010006)

摘　　要：给定一组复数{λ_i}_(i=1)^(2N-2n)(N/2≤n<N)和一个n阶广义Jacobi矩阵,构造了一个N阶广义Jacobi矩阵,使得这组给定的复数为其一部分特征值;给定的n阶广义Jacobi矩阵为其顺序主子阵,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以说明其有效性.The following problem was discussed： for N/2 ≤ n 〈 N, constructed an N x N generalized Jacobi matrix such that the given complex values, λ1 ,λ2,,……λ2N 2n, were its partial eigenvalues, and the given n x n× generalized Jaeobi matrix was its leading principal submatrix. A sufficient and neeessal7 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.

关 键 词：广义Jacob-矩阵 部分特征值 顺序主子阵 逆特征值问题 

分 类 号：O241.6[理学—计算数学]