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

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.