| 关于Jacobi矩阵的特征值反问题可解的充分必要条件的一个注记 (英) |
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| 引用本文： | 殷庆祥. 关于Jacobi矩阵的特征值反问题可解的充分必要条件的一个注记 (英)[J]. 数学研究及应用, 2007, 27(1): 107-112 |
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| 作者姓名： | 殷庆祥 |
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| 作者单位： | 盐城师范学院数学系,江苏,盐城,224002 |
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| 基金项目： | 江苏省教育厅自然科学基金 |
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| 摘 要： | 本文讨论一类具有特殊结构的Jacobi矩阵的特征值反问题,该问题由描述变截面杆的微分方程离散化得到．我们得到了这个问题有解的一些必要条件,并且通过一些数值例子,说明了L．Lu和K．Michael给出的充分条件和算法在矩阵的阶数高于3的时候是错误的。
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| 关 键 词： | 反问题 特征值反问题 Jacobi矩阵 |
| 文章编号： | 1000-341X(2007)01-0107-06 |
| 收稿时间： | 2005-04-20 |
| 修稿时间： | 2005-04-20 |
A Note on Necessary and Sufficient Conditions for the Jacobi Matrix Inverse Eigenvalue Problem |
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| YIN Qing-xiang. A Note on Necessary and Sufficient Conditions for the Jacobi Matrix Inverse Eigenvalue Problem[J]. Journal of Mathematical Research with Applications, 2007, 27(1): 107-112 |
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| Authors: | YIN Qing-xiang |
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| Affiliation: | Department of Mathematics, Yancheng Teachers College, Jiangsu 224002, China |
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| Abstract: | This paper deals with an inverse eigenvalue problem of a specially structured Jacobi matrix, which arises from the discretization of the differential equation governing the axial of a rod with varying cross section. This problem was also studied by Lu L. Z. and Sun W.W.. We give some necessary conditions for such inverse eigenvalue problem to have solutions, and present some numerical examples to show that the sufficient conditions and algorithm presented by Lu is incorrect when the order of matrix is greater than 3. |
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| Keywords: | inverse problem inverse eigenvalue problem Jacobi matrix |
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