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
于倩倩,魏广生*
YU Qian-qian, WEI Guang-sheng*
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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| [1] KREIN M G. On the spectrum of a Jacobi matrix in connection with the torsional oscillation of shafts[J]. Matematicheskii Sbornik, 1933, 40:455-466. [2] BORG G. Eine Unkehrung der Sturm-Liouvilleschen Eigenwert Aufgabe[J]. Acta Mathematica, 1946, 78(1):1-96. [3] HOCHSTADT H. On the construction of a Jacobi matrix from spectral data[J]. Linear Algebra & Its Applications, 1974, 8(5):435-446. [4] HALD O H. Inverse eigenvalue problems for Jacobi matrices[J]. Linear Algebra & its Applications, 2007, 14(1):63-85. [5] BOLEY D, GOLUB G H. A survey of matrix inverse eigenvalue problems[J]. Inverse Problems, 1999, 3(4):595-622. [6] 周树荃, 戴华. 代数特征值反问题[M]. 郑州:河南科学技术出版社, 1991. ZHOU Shuquan, DAI Hua. Inverse problem of algebra eigenvalue[M]. Zhengzhou: Henan Science and Technology Press, 1991. [7] XU Shufang. On the Jacobi matrix inverse eigenvalue problem with mixed given data[J]. Siam Journal on Matrix Analysis and Applications, 1996, 17(3):632-639. [8] LIANG Haixia, JIANG Erxiong, et al. An inverse eigenvalue problem for Jacobi matrices[J]. Computational Mathematics, 2007, 21(5):620-630. [9] WU Xiaoqian. A divide and conquer algorithm on the double dimensional inverse eigenvalue problem for Jacobi matrices[J]. Applied Mathematics & Computation, 2012, 219(8):3840-3846. [10] WEI Ying. Inverse eigenvalue problem of Jacobi matrix with mixed data[J]. Linear Algebra & Its Applications, 2015, 466(10):102-116. [11] RAM Y M. Inverse eigenvalue problem for a modified vibrating system[J]. Siam Journal on Applied Mathematics, 1993, 53(6):1762-1775. [12] NYLEN P, UHLIG F. Inverse eigenvalue problems associated with spring-mass systems[J]. Linear Algebra & its Applications, 1997, 254(1):409-425. [13] GLADWELL G M L. Inverse problems in vibration[M]. Dordrecht: Springer, 1986. [14] WEI Zhaoying, WEI Guangsheng. Inverse spectral problem for Jacobi matrices with partial spectral data[J]. Inverse Problems, 2011, 27(7):075007. |
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