一類廣義Jacobi矩陣的逆特征值問題

孟純軍

DOI：10.7612/j.issn.10002537.2017.02.012

摘要本文研究了一類廣義Jacobi矩陣的逆特征值問題，給出了該問題有解的充要條件，并討論了解的唯一性.進一步，本文給出算法計算該問題的解，數(shù)值實例說明算法是行之有效的.

關鍵詞Jacobi矩陣；廣義Jacobi矩陣；特征值；逆特征值問題

中圖分類號O241.6文獻標識碼A文章編號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