Comptes Rendus
no. 4
Numerical Analysis
Basis conversions among univariate polynomial representations
[Conversion de bases polynomiales univariées.]

Présenté par : Philippe G. Ciarlet

Roberto Barrio1 ; Juan Manuel Peña2
1 GME, Depto. Matemática Aplicada, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza, Spain
2 Depto. Matemática Aplicada, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza, Spain
Comptes Rendus. Mathématique, Volume 339 (2004) no. 4, pp. 293-298.

Dans cette Note nous fournissons une famille d'algorithmes de conversion qui met en relation les polynômes de Bernstein, les monômes et les familles classiques de polynômes orthogonaux, tels que ceux de Jacobi, Gegenbauer, Legendre, Chebyshev, Laguerre ou Hermite.

In this Note we provide a family of conversion algorithms relating Bernstein polynomials, monomials and the classical families of orthogonal polynomials, such as Jacobi, Gegenbauer, Legendre, Chebyshev, Laguerre and Hermite polynomials.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2004.06.017
Roberto Barrio 1 ; Juan Manuel Peña 2

1 GME, Depto. Matemática Aplicada, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza, Spain
2 Depto. Matemática Aplicada, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza, Spain 
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Roberto Barrio; Juan Manuel Peña. Basis conversions among univariate polynomial representations. Comptes Rendus. Mathématique, Volume 339 (2004) no. 4, pp. 293-298. doi : 10.1016/j.crma.2004.06.017. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.06.017/

[1] R. Barrio; J.M. Peña Numerical evaluation of the p-th derivative of the Jacobi series, Appl. Numer. Math., Volume 43 (2002), pp. 335-357

[2] R. Barrio, J.M. Peña, Evaluation of the derivative of a polynomial in Bernstein form, Appl. Math. Comput., in press

[3] R. Barrio; B. Melendo; S. Serrano On the numerical evaluation of linear recurrences, J. Comput. Appl. Math., Volume 150 (2003), pp. 71-86

[4] G. Farin Curves and Surfaces for Computer Aided Geometric Design, Academic Press, San Diego, 1996

[5] R.T. Farouki Legendre–Bernstein basis transformations, J. Comput. Appl. Math., Volume 119 (2000), pp. 145-160

[6] J. Hoschek; D. Lasser Fundamentals of Computer Aided Geometric Design (A.K. Peters, ed.), Wellesley, 1993

[7] Y.M. Li; X.Y. Zhang Basis conversion among Bezier, Tchebyshev and Legendre, Comput. Aided Geom. Design, Volume 15 (1998), pp. 637-642

[8] W. Magnus; F. Oberhettinger; R.P. Soni Formulas and Theorems for the Special Functions of Mathematical Physics, Springer-Verlag, 1966

[9] A. Ronveaux; A. Zarzo; E. Godoy Recurrence relations for connection coefficients between two families of orthogonal polynomials, J. Comput. Appl. Math., Volume 62 (1995), pp. 67-73

[10] B.Y. Ting; Y.L. Luke Conversion of polynomials between different polynomial bases, IMA J. Numer. Anal., Volume 1 (1981), pp. 229-234

Cité par Sources :

* The first author is supported by the Spanish Research Grant DGYCT BFM2003-02137 and the second author is supported by the Spanish Research Grant DGYCT BFM2003-03510.

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