Computing monomial interpolating basis for multivariate polynomial interpolation

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.