multivar_horner: A Python package for computing Horner factorisations of multivariate polynomials

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 (Michelfeit, 2018), the Python package presented here, is, as far as we are aware, the first open-source software for computing multivariate Horner factorisations. This paper briefly outlines the functionality of the package and places it in context with respect to previous work in the field. Benchmarks additionally demonstrate the advantages of the implementation and Horner factorisations in general.

Multivariate Interpolation on Unisolvent Nodes -- Lifting the Curse of Dimensionality

“…Recursively applying the splitting Q = Q 1 +Q H Q 2 recovers the classic Neville-Aitken evaluation algorithm [12,75,74] for dimension m = 1. Evaluation is efficiently done by applying a multivariate version of the Horner scheme, see for instance [45,86,71].…”