Our results are illustrated by some numerical examples, which show in particular the nice alternation behavior of the error function. Asymptotic Expansions for Multivariate Polynomial Approximation. Bernstein polynomials is considered. Building on recent work of Lai, we can prove that the sequence of these Bernstein polynomials possesses an asymptotic expansion with respect to the index. This generalizes a corresponding result due to Costabile, Gualtieri and Serra on univariate Bernstein polynomials, providing at the same time a new proof for it.
Numerical examples illustrate our approach.