# Linear convergence of the NQZ algorithm for finding the H-spectral radius of nonnegative tensors

## TL;DR

This paper proves the linear convergence of the NQZ algorithm for computing the H-spectral radius of certain nonnegative tensors.

## Contribution

The paper establishes linear convergence of the NQZ algorithm and provides a bound for the root convergence factor R.

## Key findings

- The NQZ algorithm converges linearly for weakly irreducible nonnegative tensors.
- An upper bound for the root convergence factor R is derived.
- A general condition for linear convergence is provided.

## Abstract

The R-linear convergence of the NQZ algorithm for computing the H-spectral radius of a class of weakly irreducible nonnegative tensors is established by utilizing the directed graphs of tensors. Meanwhile, an upper bound for the root convergence factor R is derived and a general condition ensuring the linear convergence of the NQZ algorithm is provided.