Anti-Gauss Laguerre polynomials: Some properties and a new interpolation process

Abstract

Anti-Gauss Laguerre quadrature formulas are based on the zeros of polynomials, we call them Anti-Gauss polynomials, defined in terms of Laguerre orthogonal polynomials. This paper establishes new properties of the Anti-Gauss Laguerre polynomials, and analyzes some “truncated” interpolation processes essentially based on their zeros. Estimates of the corresponding Lebesgue constants are proved, and error bounds in spaces of locally continuous functions, equipped with uniform weighted norms are given. Finally, some numerical tests are presented about the behavior of the Lebesgue functions and Lebesgue constants, and numerical experiments dealing with the approximation of functions having different smoothness are proposed. Comparisons with the results achieved by truncated Lagrange interpolation processes based on Laguerre zeros are shown.