Generalized $C^1$ quadratic B-splines generated by Merrien subdivision algorithm and some applications.
Sablonnière, Paul
HAL, hal-00001340 / Harvested from HAL
Text on HAL
A new global basis of B-splines is defined in the space of generalizedquadratic splines (GQS)generated by Merrien subdivision algorithm. Then, refinement equations forthese B-splines andthe associated corner-cutting algorithm are given. Afterwards, severalapplications arepresented. First a global construction of monotonic and/or convexgeneralized splines interpolating monotonic and/or convex data. Second,convergence of sequencesof control polygons to the graph of a GQS. Finally, a Lagrange interpolantand a quasi-interpolant which are exact on the space of affine polynomialsand whose infinitenorms are uniformly bounded independently of the partition.
Publié le : 2004-03-23
Classification:  shape preserving interpolation,  Hermite interpolation,  41A05; 41A35; 65D05; 65D17,  [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] 
@article{hal-00001340,
     author = {Sablonni\`ere, Paul},
     title = {Generalized $C^1$ quadratic B-splines generated by Merrien subdivision algorithm and some applications.},
     journal = {HAL},
     volume = {2004},
     number = {0},
     year = {2004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00001340}
}

Sablonnière, Paul. Generalized $C^1$ quadratic B-splines generated by Merrien subdivision algorithm and some applications.. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00001340/