On near-best discrete quasi-interpolation on a four-directional mesh

Authors:
D. Barrera;M. J. Ibáñez;P. Sablonnière;D. Sbibih
Affiliations:
Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, Campus Universitario de Fuentenueva s/n, 18071, Granada, Spain;Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, Campus Universitario de Fuentenueva s/n, 18071, Granada, Spain;INSA de Rennes, 20 Avenue des Buttes de Cöesmes, CS 14315, 35043 RENNES Cedex, France;Département de Mathématiques et Informatique, Faculté des Sciences, Université Mohammed 1er, 60000 OUJDA, Maroc
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

Spline quasi-interpolants are practical and effective approximation operators. In this paper, we construct QIs with optimal approximation orders and small infinity norms called near-best discrete quasi-interpolants which are based on @W-splines, i.e. B-splines with octagonal supports on the uniform four-directional mesh of the plane. These quasi-interpolants are exact on some space of polynomials and they minimize an upper bound of their infinity norms depending on a finite number of free parameters. We show that this problem has always a solution, in general nonunique. Concrete examples of such quasi-interpolants are given in the last section.