caa a22 4500 378875027 CHVBK 20180305123418.0 cr unu---uuuuu 161128s2003 xx s 000 0 eng 10.2478/cmam-2003-0038 doi (NATIONALLICENCE)gruyter-10.2478/cmam-2003-0038 Rababah Abedallah Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid 22110, Jordan. Transformation of Chebyshev-Bernstein Polynomial Basis [Elektronische Daten] [Abedallah Rababah] 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. This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. Bernstein polynomials nationallicence Chebyshev polynomials of first kind nationallicence least-squares approximation nationallicence orthogonal polynomials nationallicence basis transformation nationallicence condition number nationallicence perturbation nationallicence computer aided geometric design nationallicence Computational Methods in Applied Mathematics De Gruyter 3/4(2003), 608-622 1609-4840 3:4<608 2003 3 cmam https://doi.org/10.2478/cmam-2003-0038 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.2478/cmam-2003-0038 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Rababah Abedallah Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid 22110, Jordan NATIONALLICENCE 773 0- Computational Methods in Applied Mathematics De Gruyter 3/4(2003), 608-622 1609-4840 3:4<608 2003 3 cmam CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter