Dual generalized Bernstein basis

DOI10.1016/j.jat.2005.10.005zbMath1087.41007OpenAlexW2097566357MaRDI QIDQ818465

Paweł Woźny, Stanisław Lewanowicz

Publication date: 20 March 2006

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jat.2005.10.005

zbMATH Keywords

little \(q\)-Jacobi polynomialsBernstein basisshifted Jacobi polynomialsgeneralized Bernstein basisbig \(q\)-Jacobi polynomials\(q\)-Bernstein basis

Mathematics Subject Classification ID

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

Related Items (17)

The dual bases for the Bézier-Said-Wang type generalized Ball polynomial bases and their applications ⋮ Multi-degree reduction of tensor product Bézier surfaces with general boundary constraints ⋮ Multi-degree reduction of Bézier curves with constraints, using dual Bernstein basis polynomials ⋮ The norm estimates of the \(q\)-Bernstein operators for varying \(q>1\) ⋮ Bézier representation of the constrained dual Bernstein polynomials ⋮ Connections between two-variable Bernstein and Jacobi polynomials on the triangle ⋮ Properties of convergence for \(\omega,q\)-Bernstein polynomials ⋮ The norm estimates for the $q$-Bernstein operator in the case $q>1$ ⋮ 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 ⋮ Shape-preserving properties of \(\omega ,q\)-Bernstein polynomials ⋮ Multivariate generalized Bernstein polynomials: Identities for orthogonal polynomials of two variables ⋮ Two-variable orthogonal polynomials of big \(q\)-Jacobi type ⋮ The regularity analysis of multivariate refinable functions from generalized Bernstein bases and application in remote sensing image compression ⋮ Differential-recurrence properties of dual Bernstein polynomials ⋮ ON EXISTENCE OF SOLUTIONS FOR NONLINEAR Q-DIFFERENCE EQUATIONS WITH NONLOCAL Q-INTEGRAL BOUNDARY CONDITIONS

Cites Work

• A de Casteljau algorithm for generalized Bernstein polynomials
• The dual basis functions for the Bernstein polynomials
• Discrete Bernstein bases and Hahn polynomials
• Dual polynomial bases
• Legendre-Bernstein basis transformations
• The B-spline basis in a space of algebraic polynomials
• \(q\)-Bernstein polynomials and Bézier curves
• Convergent inversion approximations for polynomials in Bernstein form
• The special functions and their approximations. Vol. I, II
• Explicit Formula Relating the Jacobi, Hahn and Bernstein Polynomials
• Product Formulas for q-Hahn Polynomials
• Bernstein bases and hahn—eberlein orthogonal polynomials
• Formulae relating littleq-Jacobi,q-Hahn andq-Bernstein polynomials: application toq-Bézier curve evaluation
• Generalized Bernstein polynomials
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