Numerical analysis
Which spline spaces for design?
[Quelles splines utiliser pour le design ?]

Présenté par : the Editorial Board

Mazure, Marie-Laurence1
1 Laboratoire Jean Kuntzmann, Université Joseph-Fourier, BP 53, 38041 Grenoble cedex 9, France
Comptes Rendus. Mathématique, Tome 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.

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

1 Laboratoire Jean Kuntzmann, Université Joseph-Fourier, BP 53, 38041 Grenoble cedex 9, France 
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Mazure, Marie-Laurence. Which spline spaces for design?. Comptes Rendus. Mathématique, Tome 353 (2015) no. 8, pp. 761-765. doi : 10.1016/j.crma.2015.06.004. http://archive.numdam.org/articles/10.1016/j.crma.2015.06.004/

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

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

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

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

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

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

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

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

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

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

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

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

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

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