Transformation of Chebyshev–Bernstein Polynomial Basis
By Abedallah M. Rababah. 2003
54 citations recorded by the source corpus.
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.
Subfields: Computational Mechanics, Control and Systems Engineering, Signal Processing
View Paper: https://www.semanticscholar.org/paper/42dab5b03bea3fb6ce8e9d3524e84df53c14ded4
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In Computational Mechanics
In Control and Systems Engineering
In Signal Processing
Citations in the corpus
- The Bernstein polynomial basis: A centennial retrospective (2012, background): “Details on conversions between the Bernstein basis and other orthogonal polynomial bases may be found in [29, 40, 160, 161, 162].”