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-BĂ©zier 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.


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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