Construction of lattices for lagrange interpolation in projective space

Abstract

In this article we construct a lattice of points which lie on k+1 pencils of hyperplanes in the projective k-space, where, with a suitable choice of coordinate system, simple equations of the hyperplanes are obtained. This enables us to construct an interpolation formula on the projective k-space from which interpolating polynomials on a general class of lattices in the Euclidean k-space are obtained via a projective transformation. © 1991 Springer-Verlag New York Inc.