All Real Eigenvalues of Symmetric Tensors
For researchers in tensor computation, this provides a way to compute middle eigenvalues, which previously could not be found, though the method is incremental.
This paper proposes a method to compute all real eigenvalues of symmetric tensors sequentially, from largest to smallest, using Jacobian SDP relaxations in polynomial optimization. Numerical experiments demonstrate the approach.
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.