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

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. Numerical tests show the performance of the explored forms.