2004/03/23 by Sablonniere, Paul
#41A05 #41A35 #65D05 #65D17 #FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.math/0403380
A new global basis of B-splines is defined in the space of generalized quadratic splines (GQS) generated by Merrien subdivision algorithm. Then, refinement equations for these B-splines and the associated corner-cutting algorithm are given. Afterwards, several applications are presented. First a global construction of monotonic and/or convex generalized splines interpolating monotonic and/or convex data. Second, convergence of sequences of control polygons to the graph of a GQS. Finally, a Lagrange interpolant and a quasi-interpolant which are exact on the space of affine polynomials and whose infinite norms are uniformly bounded independently of the partition.