Abstract
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 A n(g) of degree ⩼ n interpolating the coefficients. We show how A n can be viewed as an inverse to the Bernstein polynomial operator and that the derivatives A n(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 A n(g) and discuss some shape preserving properties of this polynomial.
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Floater, M.S., Lyche, T. Asymptotic convergence of degree‐raising. Advances in Computational Mathematics 12, 175–187 (2000). https://doi.org/10.1023/A:1018913118047
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DOI: https://doi.org/10.1023/A:1018913118047