Please wait a minute...
北京大学期刊网 | 作者  审稿人  编委专家  工作人员

首页   |   关于   |   浏览   |   投稿指南   |   新闻公告
数学进展 - 2016, Vol. 45(6): 912-918
研究论文
非负张量Z-谱半径的上界
Upper Bounds for the Z-spectral Radius of Nonnegative Tensors

李薇1,2, 常安2
LI Wei1,2, *, CHANG An2, **

1. 福建农林大学计算机与信息学院, 福州, 福建, 350002;
2. 福州大学离散数学与计算机科学研究中心, 福州, 福建, 350003
1. School of Computer and Information Science, Fujian Agriculture and Forestry University, Fuzhou, Fujian, 350002, P. R. China;
2. Center for Discrete Mathematics and Theoretical Computer Science, Fuzhou University, Fuzhou, Fujian, 350003, P. R. China

收稿日期: 2015-05-13
出版日期: 2016-11-10
2016, Vol. 45(6): 912-918
DOI: 10.11845/sxjz.2015100b


PDF
[155 KB]
632
下载
216
浏览

引用导出
0
    /   /   推荐

摘要 

一个$m$阶 $n$维实张量是一组有$n^m$个实元素的多维数组.本文研究了非负张量最大Z-谱半径的一系列上界.

Abstract

A real $m$th-order $n$-dimensional tensor is a multidimensional array consisting of $n^m$ real entries. In this paper, new upper bounds for the Z-spectral radius of nonnegative tensors are given.

PACS:  O157.6  
[1] Berge, C., Hypergraphs, North-Holland Mathematical Library, Vol. 45, Amsterdam: North-Holland, 1989.
[2] Bul\`{o}, S.R. and Pelillo, M., New bounds on the clique number of graphs based on spectral hypergraph theory, In: Learning and Intelligent Optimization,Lecture Notes in Comput. Sci., Vol. 5851, 2009, 45-48.
[3] Cartwright, D. and Sturmfels, B., The number of eigenvalues of a tensor, Linear Algebra Appl., 2013, 438(2): 942-952.
[4] Chang, K.C., Pearson, K. and Zhang, T., Perron-Frobenius theorem for nonnegative tensors, Commun. Math. Sci., 2008, 6(2): 507-520.
[5] Chang, K.C., Qi, L.Q. and Zhang, T., A survey on the spectral theory of nonnegative tensors, Numer. Linear Algebra Appl., 2013, 20(6): 891-912.
[6] Chang, K.C. and Zhang, T., On the uniqueness and non-uniqueness of the Z-eigenvector for transition probability tensors, J. Math. Anal. Appl., 2013, 408(2): 525-540.
[7] Cooper, J. and Dutle, A., Spectra of uniform hypergraphs, Linear Algebra Appl., 2012, 436(9): 3268-3292.
[8] Hu, S.L. and Qi, L.Q., Convergence of a second order Markov chain, Appl. Math. Comput., 2014, 241: 183-192.
[9] Li, A.M., Qi, L.Q. and Zhang, B., E-characteristic polynomials of tensors, Commun. Math. Sci., 2013, 11(1): 33-53.
[10] Li, W. and Ng, M.K., On the limiting probability distribution of a transition probability tensor, Linear Multilinear Algebra}, 2014, 62(3): 362-385.(in press). DOI: 10.1080/03081087.2013.777436.
[11] Lim, L., Singular values and eigenvalues of tensors: a variational approach, In: CAMSAP2005: 1st IEEE International Workshop on Computational Advances in Multi-Tensor Adaptive Processing, Puerto Vallarta, 2005, 13/14/15: 129-132.
[12] Qi, L.Q., Eigenvalues of a real supersymmetric tensor, J. Symbolic Comput., 2005, 40(6): 1302-1324.
[13] Qi, L.Q., Wang, Y.J. and Wu, E.X., D-eigenvalues of diffusion kurtosis tensors, J. Comput. Appl. Math., 2008, 221(1): 150-157.
[14]Qi, L.Q., Yu, G.H. and Wu, E.X., Higher order positive semi-definite diffusion tensor imaging, SIAM J. Imaging Sci., 2010, 3(3): 416-433.
[15]Shao, J.Y., A general product of tensors with applications, Linear Algebra Appl., 2013, 439(8): 2350-2366.
[16] Xie, J.S. and Chang, A., On the Z-eigenvalues of the adjacency tensors for uniform hypergraphs, Linear Algebra Appl., 2013, 439(8): 2195-2204.
[17]Xie, J.S. and Chang, A., On the Z-eigenvalues of the signless Laplacian tensor for an even uniform hypergraph, Numer. Linear Algebra Appl., 2013, 20(6): 1030-1045.
[1] 罗微微, 陈建学, 张华. p2阶非正规Cayley图的核[J]. 数学进展, 2018, 47(5): 641-648.
Viewed
Full text


Abstract

Cited

  Discussed   
首页 · 关于 · 关于OA · 法律公告 · 收录须知 · 联系我们 · 注册 · 登录


© 2015-2017 北京大学图书馆 .