Anti-Gauss Lagrange interpolation: Christoffel-Darboux form, barycentric representation, and orthogonal expansion

Abstract

The paper deals with new formulations of a Lagrange interpolant polynomial based on the nodes of the well-known anti-Gauss rule. A first representation is given in terms of the classical Christoffel-Darboux kernel appropriately modified. The second one closely follows the barycentric form of the classical Lagrange polynomial, while the third formulation represents the interpolant as a combination of an orthonormal family of polynomials with respect to the discrete anti-Gauss inner product. A numerical test shows the performance of the explored forms.