Interval tensors and their application in solving multi-linear systems of equations

被引：12

作者：

Bozorgmanesh, Hassan ^{[1
]}

Hajarian, Masoud ^{[1
]}

Chronopoulos, Anthony Theodore ^{[2
,3
]}

机构：

[1] Shahid Beheshti Univ, Fac Math Sci, Dept Math, Gen Campus, Tehran 19839, Iran

[2] Univ Texas San Antonio, Dept Comp Sci, San Antonio, TX 78249 USA

[3] Univ Patras, Dept Comp Engn & Informat, Rion 26500, Greece

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2020年 / 79卷 / 03期

基金：

美国国家科学基金会;

关键词：

Interval tensor; Tensor eigenvalue bounds; Multi-linear system; Positive definite tensor; Interval Jacobi method; Interval Gauss-Seidel method; Z-EIGENVALUES; BOUNDS; REAL; ALGORITHM; SETS;

D O I：

10.1016/j.camwa.2019.07.024

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we introduce interval tensors and present some results about their eigenvalues, positive definiteness and application in solving multi-linear systems. It is proved that the set of maximum Z-eigenvalues of a symmetric interval tensor is a compact interval. Also, several bounds for eigenvalues of an interval tensor are proposed. In addition, necessary and sufficient conditions for having a positive definite interval tensor are presented and investigated. Furthermore, solving tensor equations using interval methods is presented and the interval Jacobi and Gauss-Seidel algorithms are extended for interval multi-linear systems. Finally, some numerical experiments are carried out to illustrate the methods. (C) 2019 Elsevier Ltd. All rights reserved.

引用

页码：697 / 715

页数：19

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