An Inverse Eigenvalue Problem for Jacobi Matrices

Zhengsheng Wang; Baojiang Zhong

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An Inverse Eigenvalue Problem for Jacobi Matrices

机译：Jacobi矩阵的特征值反问题

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摘要

A kind of inverse eigenvalue problem is proposed which is the reconstruction of a Jacobi matrix by given four or five eigenvalues and corresponding eigenvectors. The solvability of the problem is discussed, and some sufficient conditions for existence of the solution of this problem are proposed. Furthermore, a numerical algorithm and two examples are presented.

机译：提出了一种反特征值问题，即通过给定四个或五个特征值和相应的特征向量来重建Jacobi矩阵。讨论了该问题的可解性，并提出了解决该问题的一些充分条件。此外，给出了数值算法和两个例子。

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来源
《Mathematical Problems in Engineering》 |2011年第2期|p.1-11|共11页
作者
Zhengsheng Wang; Baojiang Zhong;
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作者单位

Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;

School of Computer Science and Technology, Soochow University, Suzhou 215006, China;

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专利

1. A survey on inverse and generalized inverse eigenvalue problems for Jacobi matrices [J] . Ghanbari K Applied mathematics and computation . 2008,第2期

机译：Jacobi矩阵的逆和广义逆特征值问题的研究
2. An inverse eigenvalue problem for pseudo-Jacobi matrices [J] . Xu Wei-Ru, Bebiano Natalia, Chen Guo-Liang Applied mathematics and computation . 2019,第期

机译：伪雅各比矩阵的逆特征值问题
3. Inverse eigenvalue problem for pseudo-symmetric Jacobi matrices with two spectra [J] . Mirzaei Hanif Linear & Multilinear Algebra: An International Journal Publishing Articles, Reviews and Problems . 2018,第1a4期

机译：具有两种光谱的伪对称Jacobi矩阵的逆特征值问题
4. THE INVERSE EIGENVALUE DETERMINANT METHOD FOR JACOBI AND TRIDIAGONAL MATRICES [C] . Patrick Dumond, Natalie Baddour Canadian Congress of Applied Mechanics . 2017

机译：Jacobi和三角形矩阵的逆特征值确定方法
5. Moment problems for Jacobi matrices and inverse problems for systems of many coupled oscillators. [D] . Gibson, Peter Campbell. 2000

机译：Jacobi矩阵的矩问题和许多耦合振荡器系统的反问题。
6. The solvability conditions for the inverse eigenvalue problem of normal skew J-Hamiltonian matrices [O] . Jia Zhao, Jieming Zhang -1

机译：正态偏J-Hamiltonian矩阵特征值反问题的可解条件
7. Large a quasi-Jacobi form for J-normal matrices and inverse eigenvalue problems [O] . Bebiano N., Furtado S., da Providência J. 2012

机译：J-正规矩阵和特征值反问题的大拟Jacobi形式
8. Matrix Inverse Eigenvalue Problem for Periodic Jacobi Matrices [R] . Boley, D. L., Golub, G. H. 1978

机译：周期Jacobi矩阵的矩阵逆特征值问题

An Inverse Eigenvalue Problem for Jacobi Matrices

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