Comptes Rendus
no. 8
Numerical analysis
Which spline spaces for design?
[Quelles splines utiliser pour le design ?]

Présenté par : the Editorial Board

Marie-Laurence Mazure1
1 Laboratoire Jean Kuntzmann, Université Joseph-Fourier, BP 53, 38041 Grenoble cedex 9, France
Comptes Rendus. Mathématique, Volume 353 (2015) no. 8, pp. 761-765.

Nous avons récemment déterminé la plus grande classe d'espaces (de fonctions suffisamment régulières) bons pour le design. Comment connecter de tels espaces pour produire la plus grande classe de « bons » espaces de splines ? Nous donnons la réponse à cette question en pointant certaines des difficultés majeures rencontrées pour l'établir.

We recently determined the largest class of spaces of sufficient regularity that are suitable for design. How can we connect different such spaces, possibly with the help of connection matrices, to produce the largest class of splines usable for design? We present the answer to this question, along with some of the major difficulties encountered to establish it. We would like to stress that the results we announce are far from being a straightforward generalisation of previous work on piecewise Chebyshevian splines.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2015.06.004
Marie-Laurence Mazure 1

1 Laboratoire Jean Kuntzmann, Université Joseph-Fourier, BP 53, 38041 Grenoble cedex 9, France 
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Marie-Laurence Mazure. Which spline spaces for design?. Comptes Rendus. Mathématique, Volume 353 (2015) no. 8, pp. 761-765. doi : 10.1016/j.crma.2015.06.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.06.004/

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[7] M.-L. Mazure Quasi-Chebyshev splines with connection matrices. Application to variable degree polynomial splines, Comput. Aided Geom. Des., Volume 18 (2001), pp. 287-298

[8] M.-L. Mazure Blossoms and optimal bases, Adv. Comput. Math., Volume 20 (2004), pp. 177-203

[9] M.-L. Mazure Ready-to-blossom bases in Chebyshev spaces (K. Jetter; M. Buhmann; W. Haussmann; R. Schaback; J. Stoeckler, eds.), Topics in Multivariate Approximation and Interpolation, vol. 12, Elsevier, 2006, pp. 109-148

[10] M.-L. Mazure Which spaces for design, Numer. Math., Volume 110 (2008), pp. 357-392

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