Abstract
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 language | English |
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Pages (from-to) | 608-622 |
Number of pages | 15 |
Journal | Computational Methods in Applied Mathematics |
Volume | 3 |
Issue number | 4 |
DOIs | |
Publication status | Published - 2003 |
Externally published | Yes |
Keywords
- 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