## Asymptotic convergence of degree-raising.(English)Zbl 0953.41004

Let $$g$$ be a polynomial of degree $$n$$ and let $$A_n(g)$$ be the polynomial of degree $$\leq n$$ interpolating the degree $$n$$ control points of $$g$$ determined by the Bernstein-Bézier coefficients of $$g$$. In this paper the authors study some results associated with $$A_n(g)$$. They show that all the derivatives of $$A_n(g)$$ converge uniformly to the corresponding derivatives of $$g$$ at the same rate $$1/n$$. They give also a refined convergence analysis of degree-raising by deriving an asymptotic expansion of Voronovskaya type. Some shape preserving properties of $$A_n(g)$$ are discussed as well.

### MSC:

 41A10 Approximation by polynomials 41A25 Rate of convergence, degree of approximation 65D17 Computer-aided design (modeling of curves and surfaces) 65D05 Numerical interpolation
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