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On Polynomial Multiplication in Chebyshev Basis [PDF]

IEEE Transactions on Computers, 2012
In a recent paper Lima, Panario and Wang have provided a new method to multiply polynomials in Chebyshev basis which aims at reducing the total number of multiplication when polynomials have small degree. Their idea is to use Karatsuba's multiplication scheme to improve upon the naive method but without being able to get rid of its quadratic complexity.
Pascal Giorgi
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Change of Basis in Polynomial Interpolation

Numerical Linear Algebra With Applications, 2005
Abstract Several representations for the interpolating polynomial exist: Lagrange, Newton, orthogonal polynomials, etc. Each representation is characterized by some basis functions. In this paper we investigate the transformations between the basis functions which map a specific representation to another.
Walter Gander
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The Bernstein Polynomial Basis: A Centennial Retrospective

Computer Aided Geometric Design, 2012
One hundred years after the introduction of the Bernstein polynomial basis, we survey the historical development and current state of theory, algorithms, and applications associated with this remarkable method of representing polynomials over finite domains.
Rida T Farouki
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A note on sparse polynomial interpolation in Dickson polynomial basis

ACM Communications in Computer Algebra, 2020
Scientific and Technological Research Council of TurkeyTurkiye Bilimsel ve Teknolojik Arastirma Kurumu (TUBITAK) [119F426]; National Science Foundation (USA)National Science Foundation (NSF) [CCF-1717100]
Erdal Imamoglu, Erich L. Kaltofen
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Gauss–Legendre polynomial basis for the shape control of polynomial curves

Applied Mathematics and Computation, 2023
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hwan Pyo Moon, Soo Hyun Kim, Song-Hwa Kwon   +2 more
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Transformation of Chebyshev–Bernstein Polynomial Basis

Computational Methods in Applied Mathematics, 2003
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 ...
Abedallah Rababah
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The Dual Basis Functions for the Bernstein Polynomials

Advances in Computational Mathematics, 1998
The Bernstein polynomials \(B^n_i\), \(i=0,1,\dots,n\) form a basis of the \((n+1)\)-dimensional real linear space \(P^n\) of all polynomials of maximal degree \(n\). The dual basis functions \(D^n_j\) with respect to the inner product of \(L^2[0,1]\) can be represented as linear combinations of the \(B^n_i\).
Bert Jüttler
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