| Jacobi矩阵特征值反问题 |
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| 引用本文： | 戴华.Jacobi矩阵特征值反问题[J].计算物理,1994,11(4):451-456. |
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| 作者姓名： | 戴华 |
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| 作者单位： | 南京航空航天大学数理力学系, 210016 |
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| 摘 要： | 研究如下一类Jacobi矩阵特征值反问题:问题IEP:给定两个互异实数λ,μ(λ<μ)和两个n维非零实向量x,y,求n阶Jacobi矩阵J,使得(λ,x),(μ,y)分别恰是J的第i,j(i≠j)个特征对。还分析了Jacobi矩阵的特征性质,给出了一个特征对恰是Jacobi矩阵J的第i个特征对的充分必要条件,由此导出了问题IEP有解的充分必要条件。
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| 关 键 词： | 特征值 特征向量 反问题 Jacobi矩阵 |
| 收稿时间： | 1993-03-19 |
| 修稿时间： | 1994-03-10 |
INVERSE EIGENVALUE PROBLEM FOR JACOBI MATRICES |
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| Dai Hua.INVERSE EIGENVALUE PROBLEM FOR JACOBI MATRICES[J].Chinese Journal of Computational Physics,1994,11(4):451-456. |
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| Authors: | Dai Hua |
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| Institution: | Nanjing Aeronautical and Astronautical University, 210016 |
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| Abstract: | The following inverse eigenvalue problem for Jacobi matrices is considered: Problem IEP.Given λ,μ∈R(λ<μ and x,y∈Rn,x≠0,y≠0, find n×n Jacobi matrix J such that (λ,x) and (μ,y) are exactly the i-th and j-th (i≠j) eigenpairs of the Jacobi matrix J, respectively. The eigenanalysis of Jacobi matrices is given. The necessary and sufficient condition is obtained for one eigenpair to be exactly the i-th eigenpair of a Jacobi matrix. Some necessary and sufficient conditions for existence of solution of the Problem IEP are given. |
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| Keywords: | characteristic value characteristic vector inverse problem Jacobi matrix |
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