# Continuation Methods for Computing Z-/H-eigenpairs of Nonnegative Tensors

## TL;DR

This paper introduces a homotopy continuation method for computing nonnegative Z- and H-eigenpairs of nonnegative tensors, guaranteeing to find a nonnegative eigenpair and analyzing the number of positive Z-eigenpairs.

## Contribution

It presents a novel homotopy continuation approach specifically designed for nonnegative tensors, with theoretical guarantees and numerical validation.

## Key findings

- Homotopy method guarantees to compute a nonnegative eigenpair.
- Number of positive Z-eigenpairs of an irreducible nonnegative tensor is odd.
- Numerical results demonstrate the effectiveness of the proposed method.

## Abstract

In this paper, a homotopy continuation method for the computation of nonnegative Z-/H-eigenpairs of a nonnegative tensor is presented. We show that the homotopy continuation method is guaranteed to compute a nonnegative eigenpair. Additionally, using degree analysis, we show that the number of positive Z-eigenpairs of an irreducible nonnegative tensor is odd. A novel homotopy continuation method is proposed to compute an odd number of positive Z-eigenpairs, and some numerical results are presented.