Multivariate polynomial interpolation under projectivities. I: Lagrange and Newton interpolation formulas (Q1186626)

The autors show that multivariate interpolation by polynomials on certain geometric systems can be treated by considering this problem on certain standard knot systems. The approach works with any system of knots such that the classical multivariate divided differences can be defined after application of a suitable perspective mapping. For such systems, both the coefficients and the basic Newton polynomials are computed recursively via multivariate divided differences.