Transformation of Chebyshev-Bernstein Polynomial Basis

Computational Methods in Applied Mathematics

Volumn 3, Issue 4, 2003, Pages 608-622

  Rababah, Abedallah ^a  

^a JORDAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Jordan)

Author keywords

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

Indexed keywords

EID: 33746245340     PISSN: 16094840     EISSN: 16099389     Source Type: Journal    
DOI: 10.2478/cmam-2003-0038     Document Type: Article

References (15)

1. T. S. Chihara, An Introduction to Orthogonal Polynomials, Gordon and Breach, New York, 1978.
2. G. Farin, Curves and Surfaces for Computer Aided Geometric Design, Academic Press, Boston, 1996.
3. R. T. Farouki, On the stability of transformations between power and Bernstein polynomial forms, Comput. Aided Geom. Des., 8 (1991), pp. 29-36.
4. R. T. Farouki, Legendre-Bernstein basis transformations, J. Comput. Appl. Math., 119 (2000), pp. 145-160.
5. R. T. Farouki and T. N. T. Goodman, On the optimal stability of Bernstein basis, Math. Comput., 65 (1996), pp. 1553-1566.
6. R. T. Farouki and V. T. Rajan, Algorithms for polynomials in Bernstein form, Comput. Aided Geom. Des., 5 (1988), pp. 1-26.
7. R. L. Graham, D. E. Knuth, and O. Patashnik, Concrete Mathematics, Addison-Wesley, Reading, MA, 1989.
8. T. Hermann, On the stability of polynomial transformations between Taylor, Bernstein and Hermite forms, Numer. Algorithms, 13 (1996), pp. 307-320.
9. J. Hoschek and D. Lasser, Fundamentals of Computer Aided Geometric Design, A. K Peters-Wellesley, 1993.
10. B. Juttler, The dual basis functions for the Bernstein polynomials, Adv. Comput. Math., 8 (1998), pp. 345-352.
11. Y. M. Lia and X. Y. Zhang, Basis conversion among Bezier, Tchebyshev and Legendre, Comput. Aided Geom. Des., 15 (1998), pp. 637-642.
12. G. G. Lorenz, Bernstein polynomials, Mathematical Expositions No. 8., Toronto Press, 1953.
13. E. D. Rainville, Special Functions, Chelsea Publ. Co., Bronx, New York, 1971.
14. J. Rice, The Approximation of Functions, Vol. 1, Linear Theory, Addison Wesley, 1964.
15. G. Szegu, Orthogonal Polynomials, 4th. ed., American Mathematical Society, Providence, RI, 1975.