The construction of multivariate polynomials with preassigned zeros

Abstract

We present an algorithm for constructing a basis of the ideal of all polynomials, which vanish at a preassigned set of points {y1,..,ym} ⊂ Kn, K a field. The algorithm yields also Newton-type polynomials for pointwise interpolation. These polynomials admit an immediate construction of interpolating polynomials and allow to shorten the algorithm, if it is applied to an enlarged set {y1,..,ym1} ⊂ Kn, m1>m.