A homotopy method for computing the largest eigenvalue of an irreducible nonnegative tensor

TL;DR

This paper introduces a homotopy method for efficiently computing the largest eigenvalue and eigenvector of an irreducible nonnegative tensor, with proven convergence and demonstrated numerical effectiveness.

Contribution

It presents a novel homotopy approach combined with a prediction-correction scheme for tensor eigenvalue computation, ensuring convergence for irreducible nonnegative tensors.

Findings

Method converges to the correct eigenpair for irreducible tensors

Numerical experiments show high efficiency of the proposed approach

The approach outperforms existing methods in speed and accuracy

Abstract

In this paper we propose a homotopy method to compute the largest eigenvalue and a corresponding eigenvector of a nonnegative tensor. We prove that it converges to the desired eigenpair when the tensor is irreducible. We also implement the method using an prediction-correction approach for path following. Some numerical results are provided to illustrate the efficiency of the method.