Near-best quasi-interpolants associated with H-splines on a three-direction mesh

Authors:
D. Barrera;M. J. Ibáñez;P. Sablonnière;D. Sbibih
Affiliations:
Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, Campus de Fuentenueva, 18071 Granada, Spain;Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, Campus de Fuentenueva, 18071 Granada, Spain;INSA de Rennes, 20 Avenue des Buttes de Coësmes, CS 14315, 35043 Rennes, Cedex, France;Département de Mathématiques et Informatique, Faculté des Sciences, Université Mohammed 1er, 60000 Oujda, Morocco
Venue:
Journal of Computational and Applied Mathematics
Year:
2005

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Abstract

Spline quasi-interpolants with optimal approximation orders and small norms are useful in several applications. In this paper, we construct the so-called near-best discrete and integral quasi-interpolants based on H-splines, i.e., B-splines with regular hexagonal supports on the uniform three-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 infinite 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 two last sections.