  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.
