Exclusion sets in the Δ-type eigenvalue inclusion set for tensors

Yaotang Li; Suhua Li

doi:10.3934/jimo.2018054

Article Contents

2019, Volume 15, Issue 2: 507-516. Doi: 10.3934/jimo.2018054

This issue Previous Article Asymptotics for a bidimensional risk model with two geometric Lévy price processes Next Article Optimal threshold strategies with capital injections in a spectrally negative Lévy risk model

Exclusion sets in the Δ-type eigenvalue inclusion set for tensors

Yaotang Li^, and
Suhua Li

School of Mathematics and Statistics, Yunnan University, Kunming 650091, China

* Corresponding author: Yaotang Li
* Corresponding author: Yaotang Li

Received: July 31, 2017

Revised: September 30, 2017

Early access: April 2018

Published: January 2019

The first author is supported by National Natural Science Foundations of China (11361074).

Abstract Full Text(HTML) Figure(3) Related Papers Cited by

Abstract

By excluding some sets which don't include any eigenvalue of a given tensor from the Δ-type eigenvalue inclusion set, two new Δ-type eigenvalue inclusion sets of tensors are given. And two criteria for identifying nonsingular tensors are also provided by using the new Δ-type eigenvalue inclusion sets.

Keywords:

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

Citation:

Full Text(HTML)

Figure 1. $C(\mathcal{A}_{0})\nsubseteqq V(\mathcal{A}_{0})$ and $C(\mathcal{A}_{0})\nsupseteqq V(\mathcal{A}_{0})$.

Download: Full-size image PowerPoint slide

Figure 2. $C(\mathcal{A}_{1})\subset \Theta(\mathcal{A}_{1})$.

Download: Full-size image PowerPoint slide

Figure 3. $V(\mathcal{A}_{2})\subset \Theta(\mathcal{A}_{2})$.

Download: Full-size image PowerPoint slide

Related Papers

Cited by

References

[1]	C. Bu, Y. Wei, L. Sun and J. Zhou, Brualdi-type eigenvalue inclusion sets of tensors, Linear Algebra and its Applications, 480 (2015), 168-175. doi: 10.1016/j.laa.2015.04.034.
[2]	C. J. Hillar and L. -H. Lim, Most tensor problems are NP-hard, Journal of the ACM (JACM), 60 (2013), Art. 45, 39 pp.
[3]	S. Hu, Z. Huang, C. Ling and L. Qi, On determinants and eigenvalue theory of tensors, Journal of Symbolic Computation, 50 (2013), 508-531. doi: 10.1016/j.jsc.2012.10.001.
[4]	Z. Huang, L. Wang, Z. Xu and J. Cui, A new S-type eigenvalue inclusion set for tensors and its applications, Journal of Inequalities and Applications, 2016 (2016), Paper No. 254, 19 pp.
[5]	C. Li, Y. Li and X. Kong, New eigenvalue inclusion sets for tensors, Numerical Linear Algebra with Applications, 21 (2014), 39-50. doi: 10.1002/nla.1858.
[6]	C. Li and Y. Li, An eigenvalue localization set for tensors with applications to determine the positive (semi-) definiteness of tensors, Linear and Multilinear Algebra, 64 (2016), 587-601. doi: 10.1080/03081087.2015.1049582.
[7]	C. Li, Z. Chen and Y. Li, A new eigenvalue inclusion set for tensors and its applications, Linear Algebra and its Applications, 481 (2015), 36-53. doi: 10.1016/j.laa.2015.04.023.
[8]	C. Li, A. Jiao and Y. Li, An S-type eigenvalue localization set for tensors, Linear Algebra and its Applications, 493 (2016), 469-483. doi: 10.1016/j.laa.2015.12.018.
[9]	C. Li, J. Zhou and Y. Li, A new Brauer-type eigenvalue localization set for tensors, Linear and Multilinear Algebra, 64 (2016), 727-736. doi: 10.1080/03081087.2015.1119779.
[10]	L. -H. Lim, Singular values and eigenvalues of tensors: A variational approach, in CAMSAP'05: Proceeding of the IEEE International Workshop on Computational Advances in MultiSensor Adaptive Processing, 2005,129–132.
[11]	L. Qi, Eigenvalues of a real supersymmetric tensor, Journal of Symbolic Computation, 40 (2005), 1302-1324. doi: 10.1016/j.jsc.2005.05.007.
[12]	L. Qi, Eigenvalues of a Supersymmetric Tensor and Positive Definiteness of an Even Degree Multivariate Form, Department of Applied Mathematics, The Hong Kong Polytechnic University, 2004.
[13]	C. Sang and J. Zhao, A new eigenvalue inclusion set for tensors with its applications, Cogent Mathematics, 4 (2017), 1320831. doi: 10.1080/23311835.2017.1320831.
[14]	X. Wang and Y. Wei, H-tensors and nonsingular H-tensors, Frontiers of Mathematics in China, 11 (2016), 557-575. doi: 10.1007/s11464-015-0495-6.
[15]	Y. Yang and Q. Yang, Further results for Perron-Frobenius theorem for nonnegative tensors, SIAM Journal on Matrix Analysis and Applications, 31 (2010), 2517-2530. doi: 10.1137/090778766.
[16]	Q. Yang and Y. Yang, Further results for Perron-Frobenius theorem for nonnegative tensors Ⅱ, SIAM Journal on Matrix Analysis and Applications, 32 (2011), 1236-1250. doi: 10.1137/100813671.