Computing tensor Z-eigenvectors with dynamical systems

Abstract

We present a new framework for computing Z-eigenvectors of general tensors based on numerically integrating a dynamical system that can only converge to a Z-eigenvector. Our motivation comes from our recent research on spacey random walks, where the long-term dynamics of a stochastic process are governed by a dynamical system that must converge to a Z-eigenvector of a transition probability tensor. Here, we apply the ideas more broadly to general tensors and find that our method can compute Z-eigenvectors that algebraic methods like the higher-order power method cannot compute.