[1]何 军,唐 兰,刘衍民.张量Z-特征值的新包含域定理[J].四川师范大学学报(自然科学版),2019,(06):799-802.[doi:10.3969/j.issn.1001-8395.2019.06.014]
 HE Jun,TANG Lan,LIU Yanmin.A New Z-eigenvalue Inclusion Theorem for Tensors[J].Journal of SichuanNormal University,2019,(06):799-802.[doi:10.3969/j.issn.1001-8395.2019.06.014]
点击复制

张量Z-特征值的新包含域定理()
分享到:

《四川师范大学学报(自然科学版)》[ISSN:1001-8395/CN:51-1295/N]

卷:
期数:
2019年06期
页码:
799-802
栏目:
基础理论
出版日期:
2019-11-04

文章信息/Info

Title:
A New Z-eigenvalue Inclusion Theorem for Tensors
文章编号:
1001-8395(2019)06-0799-04
作者:
何 军 唐 兰 刘衍民
遵义师范学院 数学学院, 贵州 遵义 563006
Author(s):
HE Jun TANG Lan LIU Yanmin
School of Mathematics, Zunyi Normal College, Zunyi 563006, Guizhou
关键词:
张量 包含域定理 Z-特征值
Keywords:
tensor inclusion theorem genvalue
分类号:
O151.21
DOI:
10.3969/j.issn.1001-8395.2019.06.014
文献标志码:
A
摘要:
张量Z-特征值问题在医学成像、判定多项式正定性等科学领域中都具有重要应用.给出张量Z-特征值的新包含域,并证明所得到的张量Z-特征值包含区域比文献(Wang G, Zhou G, Caccetta L.Discrete Contin Dyn Syst,2017,B22(1):187-198.)中定理3.4中得到的区域小.基于张量Z-特征值新包含域,得到非负张量Z-谱半径的新上界.数值例子说明结果的有效性.
Abstract:
The Z-eigenvalues of tensors play an important role in many scientific fields such as medical resonance imaging and positive definiteness of even-order multivariate forms.A new inclusion theorem for the Z-eigenvalue of tensors is given, which is always better than the results in(Wang G, Zhou G, Caccetta L.Discrete Contin Dyn Syst,2017,B22(1):187-198.)As applications, a new upper bound for the Z-spectral radius of nonnegative tensors is obtained.Numerical experiments are given to show the efficiency of our new results.tensor; inclusion theorem; Z-spectral radius of nonnegative tensors is obtained.Numerical experiments are given to show the efficiency of our new results.

参考文献/References:

[1] QI L.Eigenvalues of a real supersymmetric tensor[J].J Symbolic Comput,2005,40(6):1302-1324.
[2] ZHANG T.Existence of real eigenvalues of real tensors[J].Nonlinear Anal,2011,74(8):2862-2868.
[3] KOLDA T, MAYO J.Shifted power method for computing tensor eigenpairs[J].SIAM J Matrix Anal Appl,2011,32(4):1095-1124.
[4] CHANG K, PEARSON K, ZHANG T.Perron-Frobenius theorem for nonnegative tensors[J].Commun Math Sci,2008,6(2):507-520.
[5] YANG Y, YANG Q.Further results for Perron-Frobenius theorem for nonnegative tensors[J].SIAM J Matrix Anal Appl,2010,31(5):2517-2530.
[6] HE J, HUANG T.Upper bound for the largest Z-eigenvalue of positive tensors[J].Appl Math Lett,2014,38:110-114.
[7] LI C, LI Y, KONG X.New eigenvalue inclusion sets for tensors[J].Numer Linear Algebra Appl,2014,21(1):39-50.
[8] WANG G, ZHOU G, CACCETTA L.Z-Eigenvalue inclusion theorems for tensors[J].Discrete Contin Dyn Syst,2017,B22(1):187-198.
[9] CHANG K C, PEARSON K J, ZHANG T.Some variational principles for Z-eigenvalues of nonnegative tensors[J].Linear Algebra Appl,2013,438(11):4166-4182.

相似文献/References:

[1]何 军,刘衍民.张量广义特征值的新包含域[J].四川师范大学学报(自然科学版),2019,(02):224.[doi:10.3969/j.issn.1001-8395.2019.02.013]
 HE Jun,LIU Yanmin.New Inclusion Sets for the Generalized Tensor Eigenvalue Problem[J].Journal of SichuanNormal University,2019,(06):224.[doi:10.3969/j.issn.1001-8395.2019.02.013]
[2]桑彩丽,赵建兴*.张量E-特征值包含集及其应用[J].四川师范大学学报(自然科学版),2019,(04):485.[doi:10.3969/j.issn.1001-8395.2019.04.008]
 SANG Caili,ZHAO Jianxing.E-eigenvalue Inclusion Sets for Tensors and Their Applications[J].Journal of SichuanNormal University,2019,(06):485.[doi:10.3969/j.issn.1001-8395.2019.04.008]

备注/Memo

备注/Memo:
收稿日期:2018-05-05 接受日期:2018-09-10 基金项目:国家自然科学基金(71461027)、贵州省科技厅基础研究项目(黔科合基础[2016]1161)、贵州省教育厅自然科学基金(黔教合KY字[2016]255)和遵义市科技合作人才项目([2017]8) 第一作者简介:何 军(1981—),男,博士,副教授,主要从事数值代数的研究,E-mail:hejunfan1@163.com
更新日期/Last Update: 2019-11-04