Comptes Rendus
Numerical analysis
Which spline spaces for design?
[Quelles splines utiliser pour le design ?]
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
@article{CRMATH_2015__353_8_761_0,
     author = {Marie-Laurence Mazure},
     title = {Which spline spaces for design?},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {761--765},
     publisher = {Elsevier},
     volume = {353},
     number = {8},
     year = {2015},
     doi = {10.1016/j.crma.2015.06.004},
     language = {en},
}
TY  - JOUR
AU  - Marie-Laurence Mazure
TI  - Which spline spaces for design?
JO  - Comptes Rendus. Mathématique
PY  - 2015
SP  - 761
EP  - 765
VL  - 353
IS  - 8
PB  - Elsevier
DO  - 10.1016/j.crma.2015.06.004
LA  - en
ID  - CRMATH_2015__353_8_761_0
ER  - 
%0 Journal Article
%A Marie-Laurence Mazure
%T Which spline spaces for design?
%J Comptes Rendus. Mathématique
%D 2015
%P 761-765
%V 353
%N 8
%I Elsevier
%R 10.1016/j.crma.2015.06.004
%G en
%F CRMATH_2015__353_8_761_0
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/

[1] J.-M. Carnicer; J.-M. Peña Total positivity and optimal bases (M. Gasca; C.A. Micchelli, eds.), Total Positivity and Its Applications, Kluwer Academic Publishers, 1996, pp. 133-155

[2] P. Costantini Curve and surface construction using variable degree polynomial splines, Comput. Aided Geom. Des., Volume 17 (2000), pp. 419-446

[3] P. Costantini; T. Lyche; C. Manni On a class of weak Tchebycheff systems, Numer. Math., Volume 101 (2005), pp. 333-354

[4] T.N.T. Goodman Total positivity and the shape of curves (M. Gasca; C.A. Micchelli, eds.), Total Positivity and Its Applications, Kluwer Academic Publishers, 1996, pp. 157-186

[5] T.N.T. Goodman; M.-L. Mazure Blossoming beyond extended Chebyshev spaces, J. Approx. Theory, Volume 109 (2001), pp. 48-81

[6] P.D. Kaklis; D.G. Pandelis Convexity preserving polynomial splines of non-uniform degree, IMA J. Numer. Anal., Volume 10 (1990), pp. 223-234

[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

[11] M.-L. Mazure Ready-to-blossom bases and the existence of geometrically continuous piecewise Chebyshevian B-splines, C. R. Acad. Sci. Paris, Ser. I, Volume 347 (2009), pp. 829-834

[12] M.-L. Mazure Quasi-extended Chebyshev spaces and weight functions, Numer. Math., Volume 118 (2011), pp. 79-108

[13] M.-L. Mazure On a general new class of quasi-Chebyshevian splines, Numer. Algorithms, Volume 58 (2011) no. 3, pp. 399-438

[14] M.-L. Mazure How to build all Chebyshevian spline spaces good for geometric design, Numer. Math., Volume 119 (2011), pp. 517-556

Cité par Sources :

Commentaires - Politique