scholarly journals Change of Basis Transformation from the Bernstein Polynomials to the Chebyshev Polynomials of the Fourth Kind

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 120
Author(s):  
Abedallah Rababah ◽  
Esraa Hijazi
Keyword(s):  
Chebyshev Polynomial ◽  
Chebyshev Polynomials ◽  
Bernstein Polynomial ◽  
Bernstein Polynomials ◽  
Polynomial Basis ◽  
Bernstein Polynomial Basis ◽  
Fourth Kind

In this paper, the change of bases transformations between the Bernstein polynomial basis and the Chebyshev polynomial basis of the fourth kind are studied and the matrices of transformation among these bases are constructed. Some examples are given.

Transformation of Chebyshev–Bernstein Polynomial Basis

2003 ◽  
Vol 3 (4) ◽  
pp. 608-622 ◽  
Author(s):  
Abedallah Rababah
Keyword(s):  
Least Squares ◽  
Chebyshev Polynomials ◽  
Bernstein Polynomial ◽  
Bernstein Polynomials ◽  
Polynomial Basis ◽  
Bernstein Basis ◽  
Linear Maps ◽  
Bernstein Polynomial Basis ◽  
The Stability

AbstractIn this paper, we derive a matrix of transformation of Chebyshev polynomials of the first kind into Bernstein polynomials and vice versa. We also study the stability of these linear maps and show that the Chebyshev–Bernstein basis conversion is remarkably well-conditioned, allowing one to combine the superior least-squares performance of Chebyshev polynomials with the geometrical insight of the Bernstein form. We also compare it to other basis transformations such as Bernstein-Hermite, power-Hermite, and Bernstein–Legendre basis transformations.

Jacobi-Bernstein Basis Transformation

2004 ◽  
Vol 4 (2) ◽  
pp. 206-214 ◽  
Author(s):  
Abedallah Rababah
Keyword(s):  
Least Squares ◽  
Jacobi Polynomial ◽  
Bernstein Polynomial ◽  
Jacobi Polynomials ◽  
Polynomial Basis ◽  
Bernstein Basis ◽  
Bezier Curves ◽  
Bézier Curves ◽  
The Matrix ◽  
Bernstein Polynomial Basis

Abstract In this paper we derive the matrix of transformation of the Jacobi polynomial basis form into the Bernstein polynomial basis of the same degree n and vice versa. This enables us to combine the superior least-squares performance of the Jacobi polynomials with the geometrical insight of the Bernstein form. Application to the inversion of the Bézier curves is given.

scholarly journals Jacobi-weighted orthogonal polynomials on triangular domains

2005 ◽  
Vol 2005 (3) ◽  
pp. 205-217 ◽  
Author(s):  
A. Rababah ◽  
M. Alqudah
Keyword(s):  
Weight Function ◽  
Orthogonal Polynomials ◽  
Bernstein Polynomial ◽  
Orthogonal System ◽  
Polynomial Basis ◽  
Bernstein Basis ◽  
Triangular Domain ◽  
Jacobi Weight ◽  
Bernstein Polynomial Basis ◽  
Alpha Beta

We construct Jacobi-weighted orthogonal polynomials𝒫n,r(α,β,γ)(u,v,w),α,β,γ>−1,α+β+γ=0, on the triangular domainT. We show that these polynomials𝒫n,r(α,β,γ)(u,v,w)over the triangular domainTsatisfy the following properties:𝒫n,r(α,β,γ)(u,v,w)∈ℒn,n≥1,r=0,1,…,n,and𝒫n,r(α,β,γ)(u,v,w)⊥𝒫n,s(α,β,γ)(u,v,w)forr≠s. And hence,𝒫n,r(α,β,γ)(u,v,w),n=0,1,2,…,r=0,1,…,nform an orthogonal system over the triangular domainTwith respect to the Jacobi weight function. These Jacobi-weighted orthogonal polynomials on triangular domains are given in Bernstein basis form and thus preserve many properties of the Bernstein polynomial basis.

The Bernstein polynomial basis: A centennial retrospective

2012 ◽  
Vol 29 (6) ◽  
pp. 379-419 ◽  
Author(s):  
Rida T. Farouki
Keyword(s):  
Bernstein Polynomial ◽  
Polynomial Basis ◽  
Bernstein Polynomial Basis

scholarly journals Call option price function in Bernstein polynomial basis with no-arbitrage inequality constraints

2016 ◽  
Vol 2016 (1) ◽  
Author(s):  
Arindam Kundu ◽  
Sumit Kumar ◽  
Nutan Kumar Tomar ◽  
Shiv Kumar Gupta
Keyword(s):  
Bernstein Polynomial ◽  
Option Price ◽  
Inequality Constraints ◽  
Polynomial Basis ◽  
Call Option ◽  
No Arbitrage ◽  
Price Function ◽  
Bernstein Polynomial Basis

Bernstein polynomial basis for numerical solution of boundary value problems

2017 ◽  
Vol 77 (1) ◽  
pp. 211-228 ◽  
Author(s):  
Hamid Reza Tabrizidooz ◽  
Khadigeh Shabanpanah
Keyword(s):  
Numerical Solution ◽  
Boundary Value Problems ◽  
Bernstein Polynomial ◽  
Boundary Value ◽  
Polynomial Basis ◽  
Bernstein Polynomial Basis
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