On Aitken-Neville Formulae for Multivariate Interpolation

In a paper in J.S.I.A.M., 8, (1960), p.33–42, Thacher and Mil ne showed how the solution of certain polynomial interpolation problems in R s can be constructed from the solutions of s+1 simpler problems. In the present paper we extend the method showing that the number of basic problems to be used depends on the distribution of the points and on the chosen interpolation space, which here is not necessarily a polynomial space.