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Real eigenpairs of symmetric tensors play an important role in multipleapplications. In this paper we propose and analyze a fast iterativeNewton-based method to compute real eigenpairs of symmetric tensors. We derivesufficient conditions for a real eigenpair to be a stable fixed point for ourmethod, and prove that given a sufficiently close initial guess, theconvergence rate is quadratic. Empirically, our method converges to asignificantly larger number of eigenpairs compared to previously proposediterative methods, and with enough random initializations typically finds allreal eigenpairs. In particular, for a generic symmetric tensor, the sufficientconditions for local convergence of our Newton-based method hold simultaneouslyfor all its real eigenpairs.

Newton correction methods for computing real eigenpairs of symmetric tensors