Transformation of Chebyshev-Bernstein Polynomial Basis

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39 Citations (Scopus)


In paper [4], transformation matrices mapping the Legendre and Bernstein forms of a polynomial of degree n into each other are derived and examined. 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.

Original languageEnglish
Pages (from-to)608-622
Number of pages15
JournalComputational Methods in Applied Mathematics
Issue number4
Publication statusPublished - 2003
Externally publishedYes


  • Bernstein polynomials
  • Chebyshev polynomials of first kind
  • basis transformation
  • computer aided geometric design
  • condition number
  • least-squares approximation
  • orthogonal polynomials
  • perturbation

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics


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