Constructing Good Coefficient Functionals for Bivariate $C^1$ Quadratic Spline Quasi-Interpolants

Sara Remogna (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We consider discrete quasi-interpolants based on $C^1$ quadratic boxsplines on uniform criss-cross triangulations of a rectangular domain. The main problem consists in finding good (if not best) coefficient functionals, associated with boundary box-splines, giving both an optimal approximation order and a small infinity norm of the operator. Moreover, we want that these functionals only involve data points inside the domain. They are obtained either by minimizing their infinity norm w.r.t. a finite number of free parameters, or by inducing superconvergence of the operator at some specific points lying near or on the boundary.

Domaines: Analyse numérique [math.NA]

Sara Remogna. Constructing Good Coefficient Functionals for Bivariate $C^1$ Quadratic Spline Quasi-Interpolants. M. Daehlen, M. Floater, T. Lyche, J.-L. Merrien, K. Morken, L.L. Schumaker. Mathematical Methods for Curves and Surfaces:7th International Conference, MMCS 2008, Tønsberg, Norway, June 26-July 1, 2008, Revised Selected Papers, Springer, pp.329, 2010, Lecture Notes in Computer Science, vol. 5862, 978-3-642-11619-3. ⟨hal-00847754⟩