Transformation of Chebyshev–Bernstein Polynomial Basis

  title={Transformation of Chebyshev–Bernstein Polynomial Basis},
  author={Abedallah Rababah},
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… 

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