zbMATH — the first resource for mathematics

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)

41A10 Approximation by polynomials
Full Text: DOI
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.