Multivariate polynomial interpolation using even and odd polynomials

Abstract

The Lebesgue constant is a measure for the stability of the Lagrange interpolation. The decomposition of the Lagrange interpolation operator in their even and odd parts with respect to the last variable can be used to find a relation between the Lebesgue constant for a space of polynomials and the corresponding Lebesgue constants for subspaces of even and odd polynomials. It is shown that such a decomposition preserves the stability properties of the Lagrange interpolation operator. We use the Lebesgue functions to provide pointwise quantitative measures of the stability properties and illustrate with examples the behaviour in simple cases.