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山东大学学报(理学版) ›› 2018, Vol. 53 ›› Issue (8): 66-76.doi: 10.6040/j.issn.1671-9352.0.2018.109

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Jacobi矩阵的逆谱问题及其应用

于倩倩,魏广生*   

  1. 陕西师范大学数学与信息科学学院, 陕西 西安 710062
  • 收稿日期:2018-03-15 出版日期:2018-08-20 发布日期:2018-07-11
  • 作者简介:于倩倩(1994— ),女,硕士研究生,研究方向为微分算子谱及逆谱理论. E-mail:sddzyqq@snnu.edu.cn*通信作者简介:魏广生(1964— ),男,博士,教授,研究方向为微分算子谱及逆谱理论. E-mail: weimath@vip.sina.com
  • 基金资助:
    国家自然科学基金资助项目(11571212)

Inverse spectral problem of Jacobi matrices and its application

YU Qian-qian, WEI Guang-sheng*   

  1. College of Mathematics and Information Science, Shaanxi Normal University, Xian 710062, Shaanxi, China
  • Received:2018-03-15 Online:2018-08-20 Published:2018-07-11

摘要: 考虑Jacobi矩阵的逆谱问题。研究了在多个特殊扰动(Jn的一维扰动)的情况下, 利用所得到的特征值重构Jacobi矩阵的逆谱问题,证明了唯一确定Jacobi矩阵的逆谱定理,并将其应用到对应的质量弹簧系统, 推导出其存在唯一解的充分必要条件。给出重构的数值算法与数值例子。

关键词: Jacobi矩阵, 质量弹簧系统, 逆谱问题

Abstract: The inverse spectral problem of Jacobi matrices is considered. A new inverse spectral theorem for Jacobi matrices with some rank 1 perturbations of the matrix Jn is proved. And the theorem is applied to the corresponding mass-spring system. The necessary and sufficient conditions for the existence and uniqueness of the solution are derived. Furthermore, the numerical algorithm and some numerical examples are given.

Key words: Jacobi matrices, mass-spring system, inverse spectral problem

中图分类号: 

  • O175.9
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