The weighted dual functionals for the univariate Bernstein basis

DOI10.1016/j.amc.2006.08.065zbMath1123.41014OpenAlexW2084298329MaRDI QIDQ884627

Mohammad Al-Natour, Abedallah Rababah

Publication date: 6 June 2007

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2006.08.065

zbMATH Keywords

Bernstein polynomialsJacobi weightDual basis and functionals

Mathematics Subject Classification ID

Interpolation in approximation theory (41A05) Approximation by operators (in particular, by integral operators) (41A35)

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Modified Jacobi-Bernstein basis transformation and its application to multi-degree reduction of Bézier curves, Dual bases for Wang-Bézier basis and their applications, Bézier form of dual bivariate Bernstein polynomials, The dual bases for the Bézier-Said-Wang type generalized Ball polynomial bases and their applications, Numerical solutions of high-order differential equations with polynomial coefficients using a Bernstein polynomial basis, Multi-degree reduction of Bézier curves with constraints, using dual Bernstein basis polynomials, Bézier representation of the constrained dual Bernstein polynomials, The Bernstein polynomial basis: a centennial retrospective, A weighted extremal problem for the Bézier curves of degree \(n\) with Jacobi densities, Weighted dual functions for Bernstein basis satisfying boundary constraints, Dual basis functions in subspaces of inner product spaces, Simple algorithms for computing the Bézier coefficients of the constrained dual Bernstein polynomials, Construction of dual \(B\)-spline functions, Fast and accurate evaluation of dual Bernstein polynomials, The weighted dual functions for Wang-Bézier type generalized Ball bases and their applications, Dual basis functions for the NS-power basis and their applications, Differential-recurrence properties of dual Bernstein polynomials

Cites Work

• Algorithms for polynomials in Bernstein form
• The dual basis functions for the Bernstein polynomials
• The dual basis functions for the generalized Ball basis of odd degree
• Legendre-Bernstein basis transformations
• The B-spline basis in a space of algebraic polynomials
• Jacobi-Bernstein Basis Transformation
• Transformation of Chebyshev–Bernstein Polynomial Basis
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