Real Eigenvalues of nonsymmetric tensors
For researchers in tensor computation, this provides a method to compute eigenvalues of nonsymmetric tensors, but the contribution is incremental as it extends existing semidefinite relaxation techniques to a new class of tensors.
This paper addresses the computation of real Z-eigenvalues and H-eigenvalues of nonsymmetric tensors, proposing semidefinite relaxation methods that can compute all such eigenvalues for tensors with finitely many. The methods are demonstrated on various examples.
This paper discusses the computation of real Z-eigenvalues and H-eigenvalues of nonsymmetric tensors. A general nonsymmetric tensor has finitely many Z-eigenvalues, while there may be infinitely many ones for special tensors. In the contrast, every nonsymmetric tensor has finitely many H-eigenvalues. We propose Lasserre type semidefinite relaxation methods for computing such eigenvalues. For every nonsymmetric tensor that has finitely many real Z-eigenvalues, we can compute all of them; each of them can be computed by solving a finite sequence of semidefinite relaxations. For every nonsymmetric tensor, we can compute all its real H-eigenvalues; each of them can be computed by solving a finite sequence of semidefinite relaxations. Various examples are demonstrated.