Asymptotic convergence of degree‐raising

It is well known that the degree‐raised Bernstein–Bézier coefficients of degree n of a polynomial g converge to g at the rate 1/n. In this paper we consider the polynomial An(g) of degree ⩼ n interpolating the coefficients. We show how An can be viewed as an inverse to the Bernstein polynomial operator and that the derivatives An(g)(r) converge uniformly to g(r) at the rate 1/n for all r. We also give an asymptotic expansion of Voronovskaya type for An(g) and discuss some shape preserving properties of this polynomial.