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Pseudospectra localization sets of tensors with applications. (English) Zbl 1430.15008
Summary: A localization set and an exclusion set for the pseudospectrum of tensors are given. As applications, we first use the pseudospectra localization sets to locate asymptotically stable sets for homogeneous dynamical systems, and then two upper bounds for the largest modulus of the asymptotically stable set are given to estimate the asymptotic decay rate for homogeneous dynamical systems. We also provide two lower bounds for the preservation measure to the positive definiteness of the homogeneous polynomial form. In addition, some sufficient conditions for the global uniqueness and solvability of tensor complementarity problems are presented. The last application is to test copositivity of some potential fields in particle physics.

MSC:
15A18 Eigenvalues, singular values, and eigenvectors
15A69 Multilinear algebra, tensor calculus
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
65F10 Iterative numerical methods for linear systems
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