Near-best bivariate spline quasi-interpolants on a four-directional mesh of the plane

Domingo Barrera-Rosillo (1, 2) , Maria José Ibañez-Pérez (1) , Paul Sablonnière (3) , Driss Sbibih (4)

1 Departamento de Matemática Aplicada [Granada]
2 E-GRAN-AM - Departamento de Matematica Aplicada
3 IRMAR - Institut de Recherche Mathématique de Rennes
4 Université Mohammed Premier [Oujda]

Spline quasi-interpolants (QIs) are practical and effective approximation operators. In this paper, we construct QIs with optimal approximation orders and small infinity norms called near-best discrete and integral quasi-interpolants which are based on $\Omega$-~splines, i.e. B-splines with regular lozenge supports on the uniform four directional mesh of the plane. These quasi-interpolants are obtained so as to be exact on some space of polynomials and to minimize an upper bound of their infinity norms which depend on a finite number of free parameters. We show that this problem has always a solution, which is not unique in general. Concrete examples of these types of quasi-interpolants are given in the last section.

Mots clés: discrete quasi-interpolants; integral quasi-interpolants; near-best quasi-interpolants

Domaines: Analyse numérique [math.NA]

Domingo Barrera-Rosillo, Maria José Ibañez-Pérez, Paul Sablonnière, Driss Sbibih. Near-best bivariate spline quasi-interpolants on a four-directional mesh of the plane. 2006. ⟨hal-00072713⟩