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- W2019060010 abstract "In this paper we prove that there exists a unique positive symmetrical univariate B-spline with minimal support. It is obtained as linear combination of a minimal number of successive classical B-splines with multiple knots in the space, S r d, of cardinal polynomial splines of class C r and degree d. Next, we show that the approximation order in the space generated by the integer translates of this B-spline is not optimal. However it can be used for geometrical design where the small support is appreciated but the approximation order is not crucial. To have a higher approximation order, we deflne the B-splines of high order by recurrence and by convolution with the characteristic function of the interval (0;1). We use these B-splines to study the cardinal interpolation and we show that it is correct in the sense of Schoenberg. Finally, we give the explicit expression of interplant operators associated with some of these B-splines. Resume. Dans cet article, nous montrons l'existence et l'unicite d'une spline symetrique µ support minimal qui s'¶ecrit comme combinaison lineaire d'un nombre minimal de B-spline successives de l'espace S r des splines polynomiales cardinales de degre d et de regularite r. Nous demontrons que l'ordre d'approximation dans l'espace engendre par les translates entiµeres de cette B-spline n'est pas optimal. Cependant, leur utilisation dans le dessin geometrique, oµu l'ordre d'approximation n'est pas crucial mais oµu un support de longueur reduit est recommonde, pourrait ^ trµes utile. Pour avoir un ordre d'approximatione, nous deflnissons par recurrence de nouvelles familles de B-splines cardinales symetriques. Ensuite, nousetudions l'unisolvance du problµeme d'interpolation base sur ces B-splines. Nous donnons enfln, des exemples de calcul des coe-cients des splines fondamentales associees µ quelquesements de degres faibles de ces nouvelles familles." @default.
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- W2019060010 date "2007-01-01" @default.
- W2019060010 modified "2023-10-14" @default.
- W2019060010 title "Approximation by New Families of Univariate Symmetrical B-splines" @default.
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- W2019060010 doi "https://doi.org/10.1051/proc:072003" @default.
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