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### Jacobi矩阵的逆谱问题及其应用

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

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.

• O175.9
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