  Real eigenpairs of symmetric tensors play an important role in multiple
applications. In this paper we propose and analyze a fast iterative
Newton-based method to compute real eigenpairs of symmetric tensors. We derive
sufficient conditions for a real eigenpair to be a stable fixed point for our
method, and prove that given a sufficiently close initial guess, the
convergence rate is quadratic. Empirically, our method converges to a
significantly larger number of eigenpairs compared to previously proposed
iterative methods, and with enough random initializations typically finds all
real eigenpairs. In particular, for a generic symmetric tensor, the sufficient
conditions for local convergence of our Newton-based method hold simultaneously
for all its real eigenpairs.
