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

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