Lower bound for the Lebesgue function of an interpolation process with algebraic polynomials on equidistant nodes of a simplex

Abstract

For an interpolation process with algebraic polynomials of degree n on equidistant nodes of an m-simplex for m ≥ 2, we obtain a pointwise lower bound for the Lebesgue function similar to the well-known estimate for interpolation on a closed interval. © 2012 Pleiades Publishing, Ltd.