Computing monomial interpolating basis for multivariate polynomial interpolation

TL;DR

This paper introduces a fast method to compute the minimal monomial interpolating basis for multivariate polynomial interpolation, using a novel reverse reduced basis concept and an algorithm adaptable to any monomial ordering.

Contribution

It presents a new algorithm for efficiently computing the minimal monomial interpolating basis based on a reverse reduced basis approach, applicable to various monomial orderings.

Findings

Efficient computation of minimal monomial bases

Introduction of the reverse reduced basis concept

Applicability to different monomial orderings

Abstract

In this paper, we study how to quickly compute the <-minimal monomial interpolating basis for a multivariate polynomial interpolation problem. We address the notion of "reverse" reduced basis of linearly independent polynomials and design an algorithm for it. Based on the notion, for any monomial ordering we present a new method to read off the <-minimal monomial interpolating basis from monomials appearing in the polynomials representing the interpolation conditions.