A new modified Newton iteration for computing nonnegative Z-eigenpairs of nonnegative tensors

TL;DR

This paper introduces a modified Newton iteration method designed to efficiently compute nonnegative Z-eigenpairs of nonnegative tensors, achieving local quadratic convergence under standard assumptions.

Contribution

The paper presents a novel modification of Newton's method that guarantees local quadratic convergence for finding nonnegative eigenpairs of nonnegative tensors.

Findings

Method achieves local quadratic convergence.

Effective for nonnegative tensor eigenpair computation.

Theoretical convergence guarantees under standard assumptions.

Abstract

We propose a new modification of Newton iteration for finding some nonnegative Z-eigenpairs of a nonnegative tensor. The method has local quadratic convergence to a nonnegative eigenpair of a nonnegative tensor, under the usual assumption guaranteeing the local quadratic convergence of the original Newton iteration.