Bozorgmanesh, Hassan; Hajarian, Masoud; Chronopoulos, Anthony Theodore Interval tensors and their application in solving multi-linear systems of equations. (English) Zbl 1448.15030 Comput. Math. Appl. 79, No. 3, 697-715 (2020). Summary: 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. Cited in 6 Documents MSC: 15A69 Multilinear algebra, tensor calculus 15A18 Eigenvalues, singular values, and eigenvectors 15A06 Linear equations (linear algebraic aspects) 65F10 Iterative numerical methods for linear systems Keywords:interval tensor; tensor eigenvalue bounds; multi-linear system; positive definite tensor; interval Jacobi method; interval Gauss-Seidel method Software:PHCpack; INTLAB; PHClab PDFBibTeX XMLCite \textit{H. Bozorgmanesh} et al., Comput. Math. Appl. 79, No. 3, 697--715 (2020; Zbl 1448.15030) Full Text: DOI References: [1] Qi, L.; Luo, Z., Tensor Analysis: Spectral Theory and Special Tensors (2017), SIAM: SIAM Philadelphia · Zbl 1370.15001 [2] Qi, L., Eigenvalues of a real supersymmetric tensor, J. 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