Fast verified computation for positive solutions to M-tensor multi-linear systems and Perron vectors of a kind of weakly irreducible nonnegative tensors

2021 ◽  
pp. 113930
Author(s):  
Shinya Miyajima
Keyword(s):  
Linear Systems ◽  
Positive Solutions ◽  
Nonnegative Tensors ◽  
Verified Computation ◽  
Weakly Irreducible

scholarly journals Graphical criteria for positive solutions to linear systems

2018 ◽  
Vol 552 ◽  
pp. 166-193 ◽  
Author(s):  
Meritxell Sáez ◽  
Elisenda Feliu ◽  
Carsten Wiuf
Keyword(s):  
Linear Systems ◽  
Positive Solutions

scholarly journals The spectral symmetry of weakly irreducible nonnegative tensors and connected hypergraphs

2018 ◽  
Vol 372 (3) ◽  
pp. 2213-2233 ◽  
Author(s):  
Yi-Zheng Fan ◽  
Tao Huang ◽  
Yan-Hong Bao ◽  
Chen-Lu Zhuan-Sun ◽  
Ya-Ping Li
Keyword(s):  
Nonnegative Tensors ◽  
Weakly Irreducible

scholarly journals A modified S-type eigenvalue localization set of tensors applications

Filomat ◽  
2018 ◽  
Vol 32 (18) ◽  
pp. 6395-6416
Author(s):  
Zhengge Huang ◽  
Ligong Wang ◽  
Zhong Xu ◽  
Jingjing Cui
Keyword(s):  
Spectral Radius ◽  
Linear Algebra ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Numerical Examples ◽  
Nonnegative Tensors ◽  
Eigenvalue Localization ◽  
Localization Set ◽  
Weakly Irreducible ◽  
Eigenvalues Of Tensors

Based on the S-type eigenvalue localization set developed by Li et al. (Linear Algebra Appl. 493 (2016) 469-483) for tensors, a modified S-type eigenvalue localization set for tensors is established in this paper by excluding some sets from the existing S-type eigenvalue localization set developed by Huang et al. (arXiv: 1602.07568v1, 2016). The proposed set containing all eigenvalues of tensors is much sharper compared with that employed by Li et al. and Huang et al. As its applications, a criteria, which can be utilized for identifying the nonsingularity of tensors, is developed. In addition, we provide new upper and lower bounds for the spectral radius of nonnegative tensors and the minimum H-eigenvalue of weakly irreducible strong M-tensors. These bounds are superior to some previous results, which is illustrated by some numerical examples.

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