Please wait a minute...
浙江大学学报(理学版)  2017, Vol. 44 Issue (5): 505-510,515    DOI: 10.3785/j.issn.1008-9497.2017.05.001
数学与计算机科学     
非奇异M-矩阵Hadamard积的最小特征值的新下界
赵建兴, 桑彩丽
贵州民族大学 数据科学与信息工程学院, 贵州 贵阳 550025
New lower bounds for the minimum eigenvalue of the Hadamard product of nonsingular M-matrices
ZHAO Jianxing, SANG Caili
College of Data Science and Information Engineering, Guizhou Minzu University, Guiyang 550025, China
 全文: PDF(894 KB)   HTML  
摘要: 针对非奇异M-矩阵B与非奇异M-矩阵A的逆矩阵A-1的Hadamard 积的最小特征值τB·A-1)的估计问题,首先利用矩阵A的元素给出A-1各元素的上下界序列,然后利用这些序列和Brauer定理给出τB·A-1)单调递增收敛的下界序列.最后,通过数值算例验证理论结果,显示所得下界序列比现有结果精确,且能收敛到真值.
关键词: M-矩阵Hadamard积最小特征值下界序列    
Abstract: Let A and B be both nonsingular M-matrices, and A-1 be the inverse matrix of A. In order to get the new lower bounds of the minimum eigenvalue τ(B·A-1) of the Hadamard product of B and A-1, firstly, we give some sequences of the upper and lower bounds of the elements of A-1 are given using the elements of A.Then, using these sequences and Brauer theorem, some monotone increasing and convergent sequences of lower bounds of τ(B·A-1) are obtained. Numerical examples are provided to verify the theoretical results, which show that these sequences of the lower bounds are more accurate than some existing results and can reach the true value of the minimum eigenvalue.
Key words: M-matrix    Hadamard product    minimum eigenvalue    lower bound    sequences
收稿日期: 2015-12-13 出版日期: 2017-05-01
CLC:  O151.21  
基金资助: 国家自然科学基金资助项目(11501141);贵州省科学技术基金资助项目(黔科合J字[2015]2073号);贵州省教育厅科技拔尖人才支持项目(黔教合KY字[2016]066号).
作者简介: 赵建兴(1981-),ORCID:http://orcid.org/0000-0001-5938-3518,男,博士,副教授,主要从事数值代数研究,E-mail:zhaojianxing@gzmu.edu.cn.
服务  
把本文推荐给朋友
加入引用管理器
E-mail Alert
RSS
作者相关文章  
赵建兴
桑彩丽

引用本文:

赵建兴, 桑彩丽. 非奇异M-矩阵Hadamard积的最小特征值的新下界[J]. 浙江大学学报(理学版), 2017, 44(5): 505-510,515.

ZHAO Jianxing, SANG Caili. New lower bounds for the minimum eigenvalue of the Hadamard product of nonsingular M-matrices. Journal of Zhejiang University (Science Edition), 2017, 44(5): 505-510,515.

链接本文:

https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2017.05.001        https://www.zjujournals.com/sci/CN/Y2017/V44/I5/505

[1] 黄廷祝,杨传胜.特殊矩阵分析及应用[M].北京:科学出版社,2003. HUANG T Z, YANG C S. Special Matrix Analysis and Applications[M]. Beijing:Science Press,2003.
[2] HORN R A, JOHNSON C R. Topics in Matrix Analysis[M]. Cambridge:Cambridge University Press,1991.
[3] HIAI F, LIN M. On an eigenvalue inequality involving the Hadamard product[J]. Linear Algebra and Its Applications,2017,515:313-320.
[4] LI Y T, CHEN F B, WANG D F. New lower bounds on eigenvalue of the Hadamard product of an M-matrix and its inverse[J]. Linear Algebra and Its Applications,2009,430:1423-1431.
[5] ZHOU D M, CHEN G L, WU G X, et al. On some new bounds for eigenvalues of the Hadamard product and the Fan product of matrices[J]. Linear Algebra and Its Applications,2013,438:1415-1426.
[6] CHENG G H, TAN Q, WANG Z D. Some inequalities for the minimum eigenvalue of the Hadamard product of an M-matrix and its inverse[J]. Journal of Inequalities and Applications,2013,65:1-9.
[7] LI Y T, WANG F, LI C Q, et al. Some new bounds for the minimum eigenvalue of the Hadamard product of an M-matrix and an inverse M-matrix[J]. Journal of Inequalities and Applications,2013,480:1-8.
[8] 赵建兴,桑彩丽.非奇异矩阵的Hadamard积的最小特征值的估计[J]. 数学的实践与认识,2015,45(9):242-249. ZHAO J X, SANG C L. An sequences of the upper and lower bounds of the minimum eigenvalue of the Hadamard product for an M-matrix[J]. Mathematics in Practice and Theory,2015,45(9):242-249.
[9] CHENG G, TAN Q L, WANG Z X. Some inequalities for the Hadamard product of an M-matrix and an inverse M-matrix[J]. Journal of Inequalities and Applications,2013,2013(1):16.
[10] ZHDANOVA I V, ROGERS J, GONZALEZMARTINEZ J, et al. New inequalities for the Hadamard product of an M-matrix and its inverse[J]. Journal of Inequalities and Applications,2015,2015(1):1-12.
[1] 章茜, 蔡光辉. WOD随机变量序列加权和的完全收敛性[J]. 浙江大学学报(理学版), 2021, 48(4): 435-439.
[2] 徐惠莲, 王颖. 由渐近几乎负相协(AANA)随机变量序列生成的移动平均过程的中心极限定理[J]. 浙江大学学报(理学版), 2021, 48(1): 64-68.
[3] 宋明珠, 邵静, 刘彩云. END随机变量序列移动平均过程的极限性质[J]. 浙江大学学报(理学版), 2020, 47(5): 559-563.
[4] 高云峰, 邹广玉. NSD序列生成的移动平均过程的矩完全收敛性[J]. 浙江大学学报(理学版), 2020, 47(2): 172-177.
[5] 曾亮. 基于振荡序列的灰色GM(1,1|sin)幂模型及其应用[J]. 浙江大学学报(理学版), 2019, 46(6): 697-704.
[6] 章茜, 蔡光辉, 郑钰滟. WOD随机变量序列的完全收敛性[J]. 浙江大学学报(理学版), 2019, 46(4): 412-415.
[7] 邢峰, 邹广玉. φ-混合序列的随机中心极限定理[J]. 浙江大学学报(理学版), 2018, 45(4): 413-415.
[8] 徐怀, 唐玲. AANA序列部分和的收敛性质[J]. 浙江大学学报(理学版), 2013, 40(4): 394-400.
[9] . 基于时间序列模型分析的ADHD儿童听觉持续性注意研究[J]. 浙江大学学报(理学版), 2011, 38(6): 722-727.
[10] 王洪春. N A随机变量的指数不等式和一个强大数律 [J]. 浙江大学学报(理学版), 2000, 27(1): 20-25.
[11] 梁克维. Hansen和Patrick方法的收敛性[J]. 浙江大学学报(理学版), 1999, 26(1): 25-35.
[12] 潘建敏,张 奕. NA 序列回归函数核估计的强相合性[J]. 浙江大学学报(理学版), 1998, 25(3): 32-37.
[13] 张 艺. 一类凸规划问题的序列跟踪算法[J]. 浙江大学学报(理学版), 1996, 23(1): 1-8.