Generalized inverse spectral problem for pseudo-Jacobi matrices with mixed eigendata

被引：6
|
作者：
Xu, Wei-Ru [1 ,2 ]
Bebiano, Natalia [2 ]
Chen, Guo-Liang [1 ]
机构：
[1] East China Normal Univ, Sch Math Sci, Shanghai Key Lab Pure Math & Math Practice, Shanghai 200241, Peoples R China
[2] Univ Coimbra, Dept Math, CMUC, P-3001454 Coimbra, Portugal
来源：
INVERSE PROBLEMS IN SCIENCE AND ENGINEERING | 2019年 / 27卷 / 06期
基金：
中国国家自然科学基金;
关键词：
Generalized inverse eigenvalue problem; pseudo-Jacobi matrix; tridiagonal matrix; non-Hermitian quantum mechanics; partial spectral data; EIGENVALUE PROBLEM; CONSTRUCTION;
D O I：
10.1080/17415977.2018.1498093
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
In this paper, we investigate a generalized inverse eigenproblem for pseudo-Jacobi matrices with mixed eigendata. These matrices appear in non-Hermitian Quantum Mechanics and extend the well-known concept of Jacobi matrices. It is shown that a unique pseudo-Jacobi matrix may be recovered from certain prescribed mixed eigendata, i.e. its leading principal submatrix, two distinct real eigenvalues, and part of the corresponding eigenvectors. An algorithm is provided for the reconstruction of such a matrix, and illustrative numerical experiments are presented to test the algorithm. The recurrence relation involving leading principal minors is crucial for the problem solution.
引用
收藏
页码：773 / 789
页数：17
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