  This paper studies how to compute all real eigenvalues of a symmetric tensor.
As is well known, the largest or smallest eigenvalue can be found by solving a
polynomial optimization problem, while the other middle eigenvalues can not. We
propose a new approach for computing all real eigenvalues sequentially, from
the largest to the smallest. It uses Jacobian SDP relaxations in polynomial
optimization. We show that each eigenvalue can be computed by solving a finite
hierarchy of semidefinite relaxations. Numerical experiments are presented to
show how to do this.
