Geodesic
Approximation by New Families of Univariate Symmetrical B-splines
El Bachir Ameur1 ; Hamid Mraoui2 ; Driss Sbibih1
1 Département d'Informatique, Faculté des Sciences et Techniques, Errachidia, Maroc
2 Université Mohammed I, Ecole Supérieure de Technologie , Laboratoire MATSI, Oujda, Maroc
ESAIM. Proceedings, Tome 20 (2007), pp. 29-43.

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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, , of cardinal polynomial splines of class 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 define 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.
DOI : 10.1051/proc:072003

El Bachir Ameur 1 ; Hamid Mraoui 2 ; Driss Sbibih 1

1 Département d'Informatique, Faculté des Sciences et Techniques, Errachidia, Maroc
2 Université Mohammed I, Ecole Supérieure de Technologie , Laboratoire MATSI, Oujda, Maroc 
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     title = {Approximation by {New} {Families} of {Univariate} {Symmetrical} {B-splines}},
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El Bachir Ameur; Hamid Mraoui; Driss Sbibih. Approximation by New Families of Univariate Symmetrical B-splines. ESAIM. Proceedings, Tome 20 (2007), pp. 29-43. doi : 10.1051/proc:072003. http://geodesic.mathdoc.fr/articles/10.1051/proc:072003/

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