|
|
- 2017
非负矩阵谱半径的上界估计
|
Abstract:
非负矩阵的谱半径估计是非负矩阵理论研究的重要课题之一.如果谱半径的上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.结合非负矩阵的迹分两种情况给出非负矩阵谱半径的上界序列, 并且给出数值例子加以说明.
Estimation of the spectral radius of nonnegative matrices is an important part in the theory of nonnegative matrices. The estimates will be of greater practical value if the upper bounds of the spectral radius are expressed as a function of the element of a nonnegative matrix which is easy to calculate. In this paper, we obtain a decreasing sequence of the upper bounds for the spectral radius of a nonnegative matrix based on the trace of matrix. Numerical examples are given to illustrate the effectiveness of the method
| [1] | VARGA R S. Matrix Iterative Analysis [M]. 2版.北京:科学出版社, 2006:36. |
| [2] | 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. |
| [3] | OSTROWSKI A. Bounds for the Greatest Latent Root of a Positive Matrix[J]. London Math Soc, 1952, 27: 253-256. |
| [4] | BRAUER A. The Theorem of Ledermann and Ostrowski on Positive Matrices[J]. Duke Math J, 1957, 24: 265-274. DOI:10.1215/S0012-7094-57-02434-1 |
| [5] | LEDERMANNN W. Bounds for the Greatest Latent Root of a Positive Matrix[J]. London Math Soc, 1950, 25: 265-268. |
| [6] | 廖辉. 矩阵特征值估计的一个改进结果[J]. 西南大学学报(自然科学版), 2013, 35(6): 46-49. |
| [7] | ROJO O, SOTO R and ROJO H. A Decreasing Sequence of Eigenvalue Localization Regions[J]. Linear Algebra Appl, 1994, 196: 71-84. DOI:10.1016/0024-3795(94)90316-6 |
