A Note on the Inclusion Sets for Tensors

¹ School of Mathematics, Zunyi Normal College, Zunyi, China

² School of Mathematics, Zunyi Normal College, Zunyi, China

³ School of Mathematics, Zunyi Normal College, Zunyi, China

⁴ School of Mathematics, Zunyi Normal College, Zunyi, China

Abstract

In this paper, we give a note on the eigenvalue localization sets for tensors. We show that these sets are tighter than those provided by Li et al . (2014) [1] .

KeywordsTensor EigenvalueLocalization SetTensor

Li, C., Li, Y. and Kong, X. (2014) New Eigenvalue Inclusion Sets for Tensors. Numerical Linear Algebra with Applications, 21, 39-50. https://doi.org/10.1002/nla.1858
Chang, K.C., Pearson, K. and Zhang, T. (2008) Perron-Frobenius Theorem for Nonnegative Tensors. Communications in Mathematical Sciences, 6, 507-520. https://doi.org/10.4310/CMS.2008.v6.n2.a12
Chang, K.C., Pearson, K. and Zhang, T. (2009) On Eigenvalue Problems of Real Symmetric Tensors. Journal of Mathematical Analysis and Applications, 350, 416-422. https://doi.org/10.1016/j.jmaa.2008.09.067
Qi, L. (2007) Eigenvalues and Invariants of Tensor. Journal of Mathematical Analysis and Applications, 325, 1363-1377. https://doi.org/10.1016/j.jmaa.2006.02.071
Qi, L. (2013) Symmetric Nonnegative Tensors and Copositive Tensors. Linear Algebra and Its Applications, 439, 228-238. https://doi.org/10.1016/j.laa.2013.03.015
Ng, M.K., Qi, L. and Zhou, G. (2009) Finding the Largest Eigenvalue of a Non-Negative Tensor. SIAM Journal on Matrix Analysis and Applications, 31, 1090-1099.
Zhang, L., Qi, L. and Zhou, G. (2012) M-Tensors and the Positive Definiteness of a Multivariate Form. Preprint, arXiv:1202.6431.
Ding, W., Qi, L. and Wei, Y. (2013) M-Tensors and Nonsingular M-Tensors. Linear Algebra and Its Applications, 439, 3264-3278. https://doi.org/10.1016/j.laa.2013.08.038
Li, C., Wang, F., Zhao, J.X., Zhu, Y. and Li, Y.T. (2014) Criterions for the Positive Definiteness of Real Supersymmetric Tensors. Journal of Computational and Applied Mathematics, 255, 1-14. https://doi.org/10.1016/j.cam.2013.04.022
Qi, L. (2005) Eigenvalues of a Real Supersymmetric Tensor. Journal of Symbolic Computation, 40, 1302-1324. https://doi.org/10.1016/j.jsc.2005.05.007
Lim, L.H. (2005) Singular Values and Eigenvalues of Tensors: A Variational Approach. Proceedings of the IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP 05), Vol. 1, IEEE Computer Society Press, Piscataway, NJ, 129-132.
Li, C., Chen, Z. and Li, Y. (2015) A New Eigenvalue Inclusion Set for Tensors and Its Applications. Linear Algebra and Its Applications, 481, 36-53. https://doi.org/10.1016/j.laa.2015.04.023

Menu

A Note on the Inclusion Sets for Tensors

Abstract

References (12)