一类广义Jacobi矩阵的逆特征值问题

孟纯军

DOI：10.7612/j.issn.10002537.2017.02.012

摘要本文研究了一類广义Jacobi矩阵的逆特征值问题，给出了该问题有解的充要条件，并讨论了解的唯一性.进一步，本文给出算法计算该问题的解，数值实例说明算法是行之有效的.

关键词Jacobi矩阵；广义Jacobi矩阵；特征值；逆特征值问题

中图分类号O241.6文献标识码A文章编号10002537（2017）02007605

A Class of Inverse Eigenvalue Problems for the Generalized Jacobi Matrix

MENG Chunjun*， JIANG Tingting

（College of Mathematics and Econometrics， Hunan University， Changsha 410082， China）

AbstractIn this paper we considered a class of inverse eigenvalue problems for the generalized Jacobi matrix. The necessary and sufficient conditions under which the problem is solvable are presented. Their uniqueness is also discussed. Furthermore， we provided an algorithm to obtain the solution. Numerical examples were given to illustrate that our algorithm is both feasible and effective.

Key wordsJacobi matrix； generalized Jacobi matrix； eigenvalues； inverse eigenvalue problem