Bounds for spectral radius of nonnegative tensors using matrix-digragh-based approach

Guimin Liu; Hongbin Lv

doi:10.3934/jimo.2021176

Article Contents

2023, Volume 19, Issue 1: 105-116. Doi: 10.3934/jimo.2021176

This issue Previous Article A revised imperialist competition algorithm for cellular manufacturing optimization based on product line design Next Article Project portfolio selection based on multi-project synergy

Bounds for spectral radius of nonnegative tensors using matrix-digragh-based approach

Guimin Liu and
Hongbin Lv^,

School of Mathematics and Statistics, Beihua University, Jilin, China

^* Corresponding author: Hongbin Lv
^* Corresponding author: Hongbin Lv

Received: April 2021

Revised: August 2021

Early access: October 2021

Published: January 2023

This work is supported by the Natural Sciences Program of Science and Technology of Jilin Province of China(20190201139JC).

Abstract / Introduction Full Text(HTML) Related Papers Cited by

Abstract

We obtain the improved results of the upper and lower bounds for the spectral radius of a nonnegative tensor by its majorization matrix's digraph. Numerical examples are also given to show that our results are significantly superior to the results of related literature.

Keywords:

Mathematics Subject Classification: Primary: 15A18, 15A69.

Citation:

Full Text(HTML)

Related Papers

Cited by

References

[1]	K. C. Chang, K. Pearson and T. Zhang, Perron-Frobenius theorem for nonnegative tensors, Commun. Math. Sci., 6 (2008), 507-520. doi: 10.4310/CMS.2008.v6.n2.a12.
[2]	S. Friedland, S. Gaubert and L. Han, Peerron-Frobenius theorem for nonnegative multilinear forms and extensions, Linear Algebra Appl., 438 (2013), 738-749. doi: 10.1016/j.laa.2011.02.042.
[3]	J. He and T. Huang, Upper bound for the lagest z-eigenvalue of positive tensors, Appl. Math. Lett., 38 (2014), 110-114. doi: 10.1016/j.aml.2014.07.012.
[4]	S. L. Hu, Z. H. Huang, C. Ling and L. Qi, On determinants and eigenvalue theory of tensors, J. Symbolic Comput., 50 (2013), 508-531. doi: 10.1016/j.jsc.2012.10.001.
[5]	L. H. Lim, Singular values and eigenvalues of tensors: A Variational approach, CAMSAP '05: Proceeding of the IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, (2005), 129–132.
[6]	C. Li, Y. Wang, J. Yi and Y. Li, Bounds for the spectral radius of nonnegative tensor, J. Ind. Manag. Optim., 12 (2016), 975-990. doi: 10.3934/jimo.2016.12.975.
[7]	L. Li and C. Li, New bounds for the spectral radius for nonnegative tensors, J. Inequal. Appl., 166 (2015), 1-9. doi: 10.1186/s13660-015-0689-1.
[8]	W. Li and M. Ng, Some bounds for the spectral radius of nonnegative tensors, Numer. Math., 130 (2015), 315-335. doi: 10.1007/s00211-014-0666-5.
[9]	M. Ng, L. Qi and G. Zhou, Finding the largest eigenvalue of a nonnegative tensor, SIAM J. Matrix Anal. Appl, 31 (2009), 1090-1099. doi: 10.1137/09074838X.
[10]	K. J. Pearson, Essentially positive tensors, Int. J. Algebra, 4 (2010), 421-427.
[11]	L. Qi, Eigenvalues of a real supersymmetric tensor, J. Symbolic Comput., 40 (2005), 1302-1324. doi: 10.1016/j.jsc.2005.05.007.
[12]	L. Qi, W. Sun and Y. Wang, Numerical multilinear algebra and its applications, Front. Math. China, 2 (2007), 501-526. doi: 10.1007/s11464-007-0031-4.
[13]	L. Qi, Eigenvalues and invariants of tensors, J. Math. Anal. Appl., 325 (2007), 1363-1377. doi: 10.1016/j.jmaa.2006.02.071.
[14]	L. Qi, Y. Wang and E. Wu, D-eigenvalues of diffusion kurtosis tensors, J. Comput. Appl. Math., 221 (2008), 150-157. doi: 10.1016/j.cam.2007.10.012.
[15]	A. Roger and R. Charles, Matrix Analysis, The People's Posts and Telecommunications Press, 2007.
[16]	T. Schultz and H. Seidel, Estimating crossing fibers: A tensor decomposition approach, IEEE Transactions on Visualization and Computer Graphics, 14 (2008), 1635-1642. doi: 10.1109/TVCG.2008.128.
[17]	Y. Wang, L. Qi and X. Zhang, A practical method for computing the largest M-eigenvalue of a fourth-order partially symmetric tensor, Numer. Linear Algebra Appl., 16 (2009), 589-601. doi: 10.1002/nla.633.
[18]	Y. Yang and Q. Yang, Further results for perron-frobenius theorem for nonnegative tensors, SIAM. J. Matrix Anal. Appl., 31 (2010), 2517-2530. doi: 10.1137/090778766.