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Computational Methods in Applied Mathematics

Editor-in-Chief: Carstensen, Carsten

Managing Editor: Matus, Piotr

4 Issues per year

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Volume 4, Issue 2


Jacobi-Bernstein Basis Transformation

Abedallah Rababah
  • Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid 22110, Jordan.
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar


In this paper we derive the matrix of transformation of the Jacobi polynomial basis form into the Bernstein polynomial basis of the same degree n and vice versa. This enables us to combine the superior least-squares performance of the Jacobi polynomials with the geometrical insight of the Bernstein form. Application to the inversion of the Bézier curves is given.

Keywords: Bernstein polynomials; Jacobi polynomials; least-squares approximation; orthogonal polynomials; basis transformation; inversion of Bézier curves; computer aided geometric design

About the article

Received: 2004-01-25

Revised: 2004-03-24

Accepted: 2004-07-21

Published in Print:

Citation Information: Computational Methods in Applied Mathematics Comput. Methods Appl. Math., Volume 4, Issue 2, Pages 206–214, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: https://doi.org/10.2478/cmam-2004-0012.

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© Institute of Mathematics, NAS of Belarus. 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. BY-NC-ND 4.0

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