Interval tensors and their application in solving multi-linear systems of equations. (1st February 2020)

• Record Type: Journal Article
• Authors: Bozorgmanesh, Hassan; Hajarian, Masoud; Chronopoulos, Anthony Theodore
• Is Part Of: Computers & mathematics with applications. Volume 79:issue 3(2020)
• Page Start: 697
• Page End: 715
• Publication Date: 2020-02-01
• Subjects: Interval tensor -- Tensor eigenvalue bounds -- Multi-linear system -- Positive definite tensor -- Interval Jacobi method -- Interval Gauss–Seidel method; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2019.07.024
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: 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.