Bézier representation of the constrained dual Bernstein polynomials

DOI10.1016/j.amc.2011.10.040zbMath1243.41002arXiv1109.1169OpenAlexW1970456710MaRDI QIDQ427030

Stanisław Lewanowicz, Paweł Woźny

Publication date: 13 June 2012

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

Full work available at URL: https://arxiv.org/abs/1109.1169

zbMATH Keywords

Jacobi polynomialsHahn polynomialsconstrained dual Bernstein basisBézier polynomial formdual Bernstein basis

Mathematics Subject Classification ID

Approximation by polynomials (41A10) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45)

Related Items (17)

A note on \((p,q)\)-Bernstein polynomials and their applications based on \((p,q)\)-calculus ⋮ Bézier form of dual bivariate Bernstein polynomials ⋮ Total positivity and accurate computations with Gram matrices of Bernstein bases ⋮ On the accuracy of de Casteljau-type algorithms and Bernstein representations ⋮ Polynomial approximation of rational Bézier curves with constraints ⋮ An iterative algorithm for \(G^2\) multiwise merging of Bézier curves ⋮ Structured Inversion of the Bernstein Mass Matrix ⋮ An approximation method to circular arcs ⋮ Gram matrix of Bernstein basis: properties and applications ⋮ Efficient merging of multiple segments of Bézier curves ⋮ Degree reduction of composite Bézier curves ⋮ Explicit \(G^1\) approximation of conic sections using Bézier curves of arbitrary degree ⋮ Simple algorithms for computing the Bézier coefficients of the constrained dual Bernstein polynomials ⋮ Bernstein dual-Petrov-Galerkin method: application to 2D time fractional diffusion equation ⋮ Construction of dual \(B\)-spline functions ⋮ Fast and accurate evaluation of dual Bernstein polynomials ⋮ Differential-recurrence properties of dual Bernstein polynomials

Cites Work

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• Fast approach for computing roots of polynomials using cubic clipping
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• Dual generalized Bernstein basis
• The weighted dual functionals for the univariate Bernstein basis
• Weighted dual functions for Bernstein basis satisfying boundary constraints
• The dual basis functions for the Bernstein polynomials
• The B-spline basis in a space of algebraic polynomials
• The special functions and their approximations. Vol. I, II
• Hypergeometric Orthogonal Polynomials and Their q-Analogues
• Explicit Formula Relating the Jacobi, Hahn and Bernstein Polynomials
• Bernstein bases and hahn—eberlein orthogonal polynomials

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