Newton correction methods for computing real eigenpairs of symmetric tensors
This work addresses the problem of efficiently computing real eigenpairs of symmetric tensors, which is important in applications like signal processing and machine learning.
The paper proposes a fast iterative Newton-based method for computing real eigenpairs of symmetric tensors, achieving quadratic convergence and finding significantly more eigenpairs than previous methods, often discovering all real eigenpairs with enough random initializations.
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.