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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

(2006-05-24)

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.

1:	Universidad de Granada (E-GRANS-AM)
	Universidad de Granada
2:	Departamento de Matematica Aplicada (E-GRAN-AM)
	Universidad de Granada
3:	Institut de Recherche Mathématique de Rennes (IRMAR)
	CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne
4:	Université Mohammed 1er, Maroc (MRC-UMIS-MI)
	Université Mohammed 1er OUJDA

Subject

:

Mathematics/Numerical Analysis

Keyword(s): discrete quasi-interpolants – integral quasi-interpolants – near-best quasi-interpolants

hal-00072713, version 1

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From: Marie-Annick Guillemer <>

Submitted on: Wednesday, 24 May 2006 10:40:57

Updated on: Tuesday, 16 March 2010 14:33:29