|
|
- 2018
非负矩阵最大特征值的新界值
|
Abstract:
非负矩阵最大特征值的估计是非负矩阵理论研究的重要组成部分.如果上下界能够表示为非负矩阵元素的易于计算的函数，那么这种估计价值更高.本文通过构造两个收敛的序列得到非负矩阵最大特征值的新界值.数值算例表明其结果比有关结论更加精确.
Estimation the bounds for the greatest eigenvalue of a nonnegative matrix is important part in the theory of nonnegative matrices. It is more practical value when the bounds are expressed easily calculated function in element of matrix. New bounds for the greatest eigenvalue of a nonnegative matrix were obtained by constructing two convergent sequences. Numerical example is given to illustrate the effectiveness by comparing with the relevant conclusions
| [1] | 孙德淑. 非负矩阵Hadamard积的谱半径上界和M-矩阵Fan积的最小特征值下界的新估计[J]. 西南师范大学学报(自然科学版), 2016, 41(2): 7-11. |
| [2] | LIU S L. Bounds for the Greatest Characteristic Root of a Nonnegative Matrix[J]. Lin Alg Appl, 1996, 239(2): 151-160. |
| [3] | HORNR A, JOHNSON C R. Topic in Matrix Analysis[M]. New York: Cambrielge University Press, 1912: 465-477. |
| [4] | LEDERMANNN W. Bounds for the Greatest Latent Root of a Positive Matrix[J]. J London Math Soc, 1950(4): 265-268. |
| [5] | MINC H. Nonnegative Matrices[M]. New York: Wiley, 1988. |
| [6] | BRAUER A. The Theorems of Ledermann and Ostrowski on Positive Matrices[J]. Duke Math, 1957, 24(2): 265-274. DOI:10.1215/S0012-7094-57-02434-1 |
| [7] | 刘丽明, 黄廷祝, 刘小琴. 非负矩阵最大特征值的新界值[J]. 电子科技大学学报, 2007, 36(2): 343-345. |
