2017/06/07 by Jaffe, Ariel, Weiss, Roi, Nadler, Boaz
#15A18 #15A69 #15A72 #49M15 #FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.1706.02132
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.