Some new inequalities for the minimum H-eigenvalue of nonsingular M-tensors

Zheng Ge Huang; Li Gong Wang; Zhong Xu; Jing Jing Cui

doi:10.1016/j.laa.2018.08.023

Some new inequalities for the minimum H-eigenvalue of nonsingular M-tensors

Zheng Ge Huang, Li Gong Wang, Zhong Xu, Jing Jing Cui

School of Mathematics and Statistics

Northwestern Polytechnical University Xian

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

This paper is devoted to deriving some new upper and lower bounds for the minimum H-eigenvalue of irreducible nonsingular M-tensors. We demonstrate that the proposed bounds improve some existing ones and numerical examples are given to illustrate this fact. Additionally, we extend these bounds to general nonsingular M-tensors. The other main results in this paper is to provide sharper Ky Fan theorem and comparison theorem for nonsingular M-tensors which are better than the corresponding ones obtained by He and Huang (2014) [12].

Original language	English
Pages (from-to)	146-173
Number of pages	28
Journal	Linear Algebra and Its Applications
Volume	558
DOIs	https://doi.org/10.1016/j.laa.2018.08.023
State	Published - 1 Dec 2018

Keywords

Comparison theorem
Ky Fan theorem
Minimum H-eigenvalue
Nonsingular M-tensors

Access to Document

10.1016/j.laa.2018.08.023

Cite this

@article{861b7563616849d8a20346212e263a75,

title = "Some new inequalities for the minimum H-eigenvalue of nonsingular M-tensors",

abstract = "This paper is devoted to deriving some new upper and lower bounds for the minimum H-eigenvalue of irreducible nonsingular M-tensors. We demonstrate that the proposed bounds improve some existing ones and numerical examples are given to illustrate this fact. Additionally, we extend these bounds to general nonsingular M-tensors. The other main results in this paper is to provide sharper Ky Fan theorem and comparison theorem for nonsingular M-tensors which are better than the corresponding ones obtained by He and Huang (2014) [12].",

keywords = "Comparison theorem, Ky Fan theorem, Minimum H-eigenvalue, Nonsingular M-tensors",

author = "Huang, {Zheng Ge} and Wang, {Li Gong} and Zhong Xu and Cui, {Jing Jing}",

note = "Publisher Copyright: {\textcopyright} 2018 Elsevier Inc.",

year = "2018",

month = dec,

day = "1",

doi = "10.1016/j.laa.2018.08.023",

language = "英语",

volume = "558",

pages = "146--173",

journal = "Linear Algebra and Its Applications",

issn = "0024-3795",

publisher = "Elsevier Inc.",

}

TY - JOUR

T1 - Some new inequalities for the minimum H-eigenvalue of nonsingular M-tensors

AU - Huang, Zheng Ge

AU - Wang, Li Gong

AU - Xu, Zhong

AU - Cui, Jing Jing

PY - 2018/12/1

Y1 - 2018/12/1

N2 - This paper is devoted to deriving some new upper and lower bounds for the minimum H-eigenvalue of irreducible nonsingular M-tensors. We demonstrate that the proposed bounds improve some existing ones and numerical examples are given to illustrate this fact. Additionally, we extend these bounds to general nonsingular M-tensors. The other main results in this paper is to provide sharper Ky Fan theorem and comparison theorem for nonsingular M-tensors which are better than the corresponding ones obtained by He and Huang (2014) [12].

AB - This paper is devoted to deriving some new upper and lower bounds for the minimum H-eigenvalue of irreducible nonsingular M-tensors. We demonstrate that the proposed bounds improve some existing ones and numerical examples are given to illustrate this fact. Additionally, we extend these bounds to general nonsingular M-tensors. The other main results in this paper is to provide sharper Ky Fan theorem and comparison theorem for nonsingular M-tensors which are better than the corresponding ones obtained by He and Huang (2014) [12].

KW - Comparison theorem

KW - Ky Fan theorem

KW - Minimum H-eigenvalue

KW - Nonsingular M-tensors

UR - http://www.scopus.com/inward/record.url?scp=85051822670&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2018.08.023

DO - 10.1016/j.laa.2018.08.023

M3 - 文章

AN - SCOPUS:85051822670

SN - 0024-3795

VL - 558

SP - 146

EP - 173

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Some new inequalities for the minimum H-eigenvalue of nonsingular M-tensors

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this