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On dual functionals of polynomials in B-form. (English) Zbl 0738.41014
The space of polynomials in \(B\)-form, i.e. polynomials in Bernstein, Bézier, or de Casteljan representation, is considered. The author gives an explicit representation of its dual space. Using this space, the \(B\)- form of a monomial is expressed. The author gives a simple algorithm to convert a polynomial from its Taylor expansion to its \(B\)-form. Upper bounds for the basis element of the dual space are obtained and using these bounds the author improves some known estimates by giving explicit constants.
Reviewer: K.Najzar (Praha)

MSC:
41A10 Approximation by polynomials
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[1] \scP. J. Barry and R. N. Goldman, Three examples of dual properties of Bézier Curves. in “Mathematical Methods in CAGD” (T. Lyche and L. L. Schumaker, Eds.), pp. 61-69, Academic Press, Orlando, FL.
[2] Böhm, W; Farin, G; Kahmann, J, A survey of curve and surface methods in CAGD, Comput. aided geom. design, 1, 1-60, (1984) · Zbl 0604.65005
[3] de Boor, C, B-form basics, (), 131-148
[4] de Boor, C; Höllig, K, Approximation power of smooth bivariate pp functions, Math. Z., 197, 343-363, (1988) · Zbl 0616.41010
[5] Chui, C.K, Multivariate splines, () · Zbl 0619.41004
[6] Chui, C.K; Lai, M.J, On bivariate super vertex splines, Constr. approx., 6, 399-419, (1990) · Zbl 0726.41012
[7] Chui, C.K; Lai, M.J, On bivariate vertex splines, (), 84-115 · Zbl 0588.65009
[8] Chui, C.K; Lai, M.J, Multivariate splines and finite elements, J. approx. theory, 60, 245-343, (1990) · Zbl 0702.41017
[9] Dahmen, W, Bernstein-Bézier representation of polynomial surfaces, (), organized by C. de Boor, Dallas · Zbl 0606.41009
[10] Farin, G, Subsplines über dreiecken, ()
[11] Farin, G, Bézier polynomials over triangles and the construction of piecewise C^r-polynomials, ()
[12] Farin, G, Triangular Bernstein-Bézier patches, Comput. aided geom. design, 3, 87-127, (1986)
[13] Zhou, K; Sun, J, Dual bases of multivariate Bernstein-Bézier polynomials, Comput. aided geom. design, 5, 119-125, (1988) · Zbl 0642.41005
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