# Constructive methods for spectra with three nonzero elements in the nonnegative inverse eigenvalue problem

## TL;DR

This paper introduces and compares three constructive methods for realizing non-real spectra with three nonzero elements in the nonnegative inverse eigenvalue problem, providing necessary conditions and numerical examples.

## Contribution

The paper presents new constructive methods and necessary conditions for realizing specific non-real spectra in the nonnegative inverse eigenvalue problem.

## Key findings

- Three constructive methods for spectra realization
- Necessary conditions for realizability
- Numerical examples demonstrating methods

## Abstract

We present and compare three constructive methods for realizing non-real spectra with three nonzero elements in the nonnegative inverse eigenvalue problem. We also provide some necessary conditions for realizability and numerical examples. In particular, we utilise the companion matrix.