Computing tensor Z-eigenvectors with dynamical systems
Numerical Analysis
2019-03-14 v3 Numerical Analysis
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.
Keywords
Cite
@article{arxiv.1805.00903,
title = {Computing tensor Z-eigenvectors with dynamical systems},
author = {Austin R. Benson and David F. Gleich},
journal= {arXiv preprint arXiv:1805.00903},
year = {2019}
}