| Jacobi矩阵的逆谱问题及其应用 |
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| 引用本文： | 于倩倩,魏广生.Jacobi矩阵的逆谱问题及其应用[J].山东大学学报(理学版),2018,53(8):66-76. |
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| 作者姓名： | 于倩倩 魏广生 |
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| 作者单位： | 陕西师范大学数学与信息科学学院, 陕西 西安 710062 |
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| 基金项目： | 国家自然科学基金资助项目(11571212) |
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| 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。
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| 关 键 词： | Jacobi矩阵 质量弹簧系统 逆谱问题 |
| 收稿时间： | 2018-03-15 |
Inverse spectral problem of Jacobi matrices and its application |
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| YU Qian-qian,WEI Guang-sheng.Inverse spectral problem of Jacobi matrices and its application[J].Journal of Shandong University,2018,53(8):66-76. |
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| Authors: | YU Qian-qian WEI Guang-sheng |
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| Institution: | College of Mathematics and Information Science, Shaanxi Normal University, Xian 710062, Shaanxi, China |
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| 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. |
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| Keywords: | Jacobi matrices mass-spring system inverse spectral problem |
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