multivar_horner: a python package for computing Horner factorisations of multivariate polynomials

TL;DR

The paper introduces multivar_horner, an open-source Python package that efficiently computes Horner factorisations of multivariate polynomials, improving numerical stability and computational efficiency in scientific applications.

Contribution

It presents the first open-source tool for multivariate Horner factorisations, with benchmarks demonstrating its advantages over previous methods.

Findings

The package enables stable and efficient polynomial evaluation.

Benchmarks show performance improvements over existing approaches.

Horner factorisations enhance numerical stability in scientific computations.

Abstract

Many applications in the sciences require numerically stable and computationally efficient evaluation of multivariate polynomials. Finding beneficial representations of polynomials, such as Horner factorisations, is therefore crucial. multivar_horner, the python package presented here, is the first open source software for computing multivariate Horner factorisations. This work briefly outlines the functionality of the package and puts it into reference to previous work in the field. Benchmarks additionally prove the advantages of the implementation and Horner factorisations in general.