[1]田朝薇,宋海洲.正矩阵最大特征值界的新估计[J].华侨大学学报(自然科学版),2009,30(2):237-238.[doi:10.11830/ISSN.1000-5013.2009.02.0237]
　TIAN Zhao-wei,SONG Hai-zhou.New Estimation for the Bounds of the Greatest Characteristic Root of a Positive Matrix[J].Journal of Huaqiao University(Natural Science),2009,30(2):237-238.[doi:10.11830/ISSN.1000-5013.2009.02.0237]
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正矩阵最大特征值界的新估计()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第30卷
期数:
2009年第2期
页码:
237-238
栏目:
出版日期:
2009-03-20

文章信息/Info

Title:
New Estimation for the Bounds of the Greatest Characteristic Root of a Positive Matrix
文章编号:
1000-5013(2009)02-0237-02
作者:
田朝薇; 宋海洲
华侨大学数学科学学院
Author(s):
TIAN Zhao-wei;  SONG Hai-zhou
School of Mathematics Sciences, Huaqiao University, Quanzhou 362021, China
关键词:
正矩阵;  特征值;  新估计;  界;  谱半径
Keywords:
positive matrix;  eigenvalue;  bounds;  new estimation;  spectral radius
分类号:
O151.21
DOI:
10.11830/ISSN.1000-5013.2009.02.0237
文献标志码:
A
摘要:
利用Frobenius定理、相似变换及一些不等式技巧,得到正矩阵谱半径的新上、下界.结果表明,新上界比Ostrowski定理的上界更优; 在某些条件下,新上界优于Brauer定理的上界.最后,用实例证明结果.
Abstract:
In this paper,we obtain new bounds for the greatest eigenvalues of a positive matrix by using Frobenius theorem,similarity transformation and the skill of inequation.The new upper bound is sharper than the upper bound in Ostrowski theorem.And in certain condition,the new upper bound is better than Brauer’s.Some examples are given to show that the new estimation method is effective.

参考文献/References:

[1] FROBENIUS G. ber matrizen aus nichtnegativen elementen [M]. Berlin:Sitzungsber Knuss Akad Wiss, 1912.456-477.
[2] OSTROWSKI A. Bounds for the greatest latent root of a positive matrix [J]. Journal of the London Mathematical Society, 1952.253-256.doi:10.1112/jlms/s1-27.2.253.
[3] BRAUER A. The theorems of ledermann and ostrowski on positive matrixes [J]. Duke Mathematical Journal, 1957.265-274.
[4] 秦霁, 黄廷祝. 非负矩阵Perron根的下界 [J]. 工程数学学报, 2007(3):559-562.doi:10.3969/j.issn.1005-3085.2007.03.026.
[5] 卢琳璋, 马飞. 非负矩阵Perron根的上下界 [J]. 计算数学, 2003(2):58-64.doi:10.3321/j.issn:0254-7791.2003.02.007.

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更新日期/Last Update: 2014-03-23