JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2018, Vol. 53 ›› Issue (8): 66-76.doi: 10.6040/j.issn.1671-9352.0.2018.109

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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.

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

CLC Number: 

  • O175.9
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