Mean convergence of extended Lagrange interpolation with Freud weights
The mean convergence of Lagrange interpolation at the zeros of the orthonormal polynomials associated with the Freud weight has been extensively studied. Considering two additional points of interpolation \textit{J. Szabados} [J. Inequal. Appl. 1, No. 2, 99-123 (1997; Zbl 0916.41002)] has indeed shown that the Lebesgue constant does not grow faster than log \(n\). The authors show that a similar advantage is achieved in the mean convergence of Lagrange interpolation if the foregoing extended nodes are considered in place of just the zeros of the orthogonal polynomials.
scientific article; zbMATH DE number 1404413