Transformation of Chebyshev–Bernstein Polynomial Basis
Abstract: In 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.
- Standort
-
Deutsche Nationalbibliothek Frankfurt am Main
- Umfang
-
Online-Ressource
- Sprache
-
Englisch
- Erschienen in
-
Transformation of Chebyshev–Bernstein Polynomial Basis ; volume:3 ; number:4 ; year:2003 ; pages:608-622
Computational methods in applied mathematics ; 3, Heft 4 (2003), 608-622
- Urheber
- DOI
-
10.2478/cmam-2003-0038
- URN
-
urn:nbn:de:101:1-2410261611338.182862568510
- Rechteinformation
-
Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Letzte Aktualisierung
-
15.08.2025, 07:37 MESZ
Datenpartner
Dieses Objekt wird bereitgestellt von:
Deutsche Nationalbibliothek. Bei Fragen zum Objekt wenden Sie sich bitte an den Datenpartner.
Deutsche Nationalbibliothek. Bei Fragen zum Objekt wenden Sie sich bitte an den Datenpartner.
Beteiligte
Ähnliche Objekte (12)
On the Chebyshev Norm of Polynomial B-Splines
Jacobi-Bernstein Basis Transformation
Chebyshev polynomial-based Fourier transformation and its use in low pass filter of gravity data
Numerical Solutions of High-Order Differential Equations with Polynomial Coefficients Using a Bernstein Polynomial Basis
An efficient image encryption scheme based on fractal Tromino and Chebyshev polynomial
Call option price function in Bernstein polynomial basis with no-arbitrage inequality constraints
Asymptotics of Polynomial Interpolation and the Bernstein Constants
![Chebyshev & [and] Fourier spectral methods](/assets/placeholder/searchResultMediaNoDigitisedMedia.png)
Chebyshev & [and] Fourier spectral methods
Chebyshev splines and Kolmogorov inequalities
On Chebyshev polynomials of matrices
Analysis of coordinate transformation with different polynomial models
On the reduced Bernstein-Sato polynomial of Thom-Sebastiani singularities
On the Chebyshev Norm of Polynomial B-Splines
Jacobi-Bernstein Basis Transformation
Chebyshev polynomial-based Fourier transformation and its use in low pass filter of gravity data
Numerical Solutions of High-Order Differential Equations with Polynomial Coefficients Using a Bernstein Polynomial Basis
An efficient image encryption scheme based on fractal Tromino and Chebyshev polynomial
Call option price function in Bernstein polynomial basis with no-arbitrage inequality constraints
Asymptotics of Polynomial Interpolation and the Bernstein Constants
Chebyshev & [and] Fourier spectral methods
Chebyshev splines and Kolmogorov inequalities
On Chebyshev polynomials of matrices
Analysis of coordinate transformation with different polynomial models
On the reduced Bernstein-Sato polynomial of Thom-Sebastiani singularities
On the Chebyshev Norm of Polynomial B-Splines
Jacobi-Bernstein Basis Transformation
Chebyshev polynomial-based Fourier transformation and its use in low pass filter of gravity data
Numerical Solutions of High-Order Differential Equations with Polynomial Coefficients Using a Bernstein Polynomial Basis
An efficient image encryption scheme based on fractal Tromino and Chebyshev polynomial
Call option price function in Bernstein polynomial basis with no-arbitrage inequality constraints
Asymptotics of Polynomial Interpolation and the Bernstein Constants
Chebyshev & [and] Fourier spectral methods
Chebyshev splines and Kolmogorov inequalities
On Chebyshev polynomials of matrices
Analysis of coordinate transformation with different polynomial models