Eigenvalue bounds of third-order tensors via the minimax eigenvalue of symmetric matrices

被引：12

作者：

Li, Shigui ^{[1
]}

Chen, Zhen ^{[1
]}

Li, Chaoqian ^{[2
]}

Zhao, Jianxing ^{[3
]}

机构：

[1] Guizhou Normal Univ, Sch Math Sci, Guiyang 550025, Peoples R China

[2] Yunnan Univ, Sch Math & Stat, Kunming 650091, Yunnan, Peoples R China

[3] Guizhou Minzu Univ, Coll Data Sci & Informat Engn, Guiyang 550025, Peoples R China

来源：

COMPUTATIONAL & APPLIED MATHEMATICS | 2020年 / 39卷 / 03期

基金：

中国国家自然科学基金;

关键词：

H-eigenvalues; Z-eigenvalues; C-eigenvalues; Nonsingular M-tensors; Tensor complementarity problems; Piezoelectric-type tensors; 15A18; 15A42; 15A69; SOLVING MULTILINEAR SYSTEMS; POLYADIC DECOMPOSITION; OPERATORS; SETS;

D O I：

10.1007/s40314-020-01245-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Upper and lower bounds for H-eigenvalues, Z-spectral radius and C-spectral radius of a third-order tensor are given by the minimax eigenvalue of symmetric matrices extracted from this given tensor. As applications, a sufficient condition for third-order nonsingular M-tensors and some valid sufficient conditions for the uniqueness and solvability of the solutions to multi-linear systems, tensor complementarity problems and non-homogeneous systems are proposed.

引用

页数：14

共 50 条

[1] Eigenvalue bounds of third-order tensors via the minimax eigenvalue of symmetric matrices
Shigui Li
Zhen Chen
Chaoqian Li
Jianxing Zhao
Computational and Applied Mathematics, 2020, 39
[2] A study on the C-eigenvalue of the third-order tensors
Liu, Jie
Liu, Xiaoji
Jin, Hongwei
Wang, Hongxing
COMPUTATIONAL & APPLIED MATHEMATICS, 2025, 44 (01):
[3] CANONICAL POLYADIC DECOMPOSITION OF THIRD-ORDER TENSORS: REDUCTION TO GENERALIZED EIGENVALUE DECOMPOSITION
Domanov, Ignat
De Lathauwer, Lieven
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2014, 35 (02) : 636 - 660
[4] An Inverse Eigenvalue Problem for a Class of Second- and Third-Order Matrices
Perepelkin, E. A.
NUMERICAL ANALYSIS AND APPLICATIONS, 2015, 8 (03) : 260 - 266
[5] Eigenvalue bounds for symmetric matrices with entries in one interval
Leng, Huinan
He, Zhiqing
APPLIED MATHEMATICS AND COMPUTATION, 2017, 299 : 58 - 65
[6] Filtering algorithm for eigenvalue bounds of fuzzy symmetric matrices
Mahato, Nisha Rani
Chakraverty, Snehashish
ENGINEERING COMPUTATIONS, 2016, 33 (03) : 855 - 875
[7] C-EIGENVALUE INTERVALS FOR PIEZOELECTRIC-TYPE TENSORS VIA SYMMETRIC MATRICES
Liu, Xifu
Yin, Shuheng
Li, Hanyu
JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION, 2021, 17 (06) : 3349 - 3356
[8] Tetrahedral Frame Fields via Constrained Third-Order Symmetric Tensors
Dmitry Golovaty
Matthias Kurzke
Jose Alberto Montero
Daniel Spirn
Journal of Nonlinear Science, 2023, 33
[9] Tetrahedral Frame Fields via Constrained Third-Order Symmetric Tensors
Golovaty, Dmitry
Kurzke, Matthias
Montero, Jose Alberto
Spirn, Daniel
JOURNAL OF NONLINEAR SCIENCE, 2023, 33 (03)
[10] Projection Scheme and Adaptive Control for Symmetric Matrices With Eigenvalue Bounds
Moghe, Rahul
Akella, Maruthi R.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2023, 68 (03) : 1738 - 1745

← 1 2 3 4 5 →