The paper deals with a special filtered approximation method, which originates interpolation polynomials at Chebyshev zeros by using de la Vallée Poussin filters. In order to get an optimal in spaces of locally continuous functions equipped weighted uniform norms, the related Lebesgue constants have be uniformly bounded. previous works this has already been proved under different sufficient con...

In this paper we study multivariate polynomial interpolation on lower sets of points. A lower set can be expressed as the union of blocks of points. We show that a natural interpolant on a lower set can be expressed as a linear combination of tensor-product interpolants over various intersections of the blocks that define it. Math Subject Classification: 41A05, 41A10, 65D05

We present an eecient version of the Horner scheme for the evaluation of multivariate polynomials and study its stability properties. In particular, we show that the backward error of evaluation is bounded by a quantity that is linear in the total degree of the polynomial, which itself is usually signiicantly smaller than the number of operation involved in the evaluation process. Moreover, we ...

This paper summarizes relations between the constructive theory of polynomial ideals and polynomial interpolation in several variables. The main ingredient is a generalization of the algorithm for division with remainder to \quotients" of polynomials and nite sets of polynomi-als. x1. Introduction When compared to the univariate case, polynomial interpolation in several variables turns out to b...