On near-best discrete quasi-interpolation on a four-directional mesh
type: Item
instance of: scholarly article
title: On near-best discrete quasi-interpolation on a four-directional mesh
zbMATH Open document ID: 1184.41007
author: M. J. Ibáñez
author: D. Barrera
author: P. Sablonnière
author: D. Sbibih
published in: Journal of Computational and Applied Mathematics
publication date: 2009-12-18T00:00:00Z
review text: Quasi-interpolation in two dimensions, for example, is a highly useful alternative to interpolation from spline or other function spaces. Its advantage is that no interpolation coefficients have to be computed; however, its construction depends on the choice of the linear operator which is to be applied to the approximand so that the quasi-interpolation can take place. (An example is a simple function evaluation at various points. Generally, only discrete operators are used in this article.) In this paper, the quasi-interpolants stem from polynomial spline spaces defined by four-direction meshes in two dimensions, and they are constructed to minimize the norm of the quasi-interpolation operator (comparable to the Lebesgue constant of the interpolation operator). It is in this sense that the quasi-interpolation is chosen -- as stated in the title -- to be near-best.
reviewed by: Martin D. Buhmann
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 65D07
zbMATH DE Number: 5650064
zbMATH Keywords: \(\Omega \)-splines
zbMATH Keywords: discrete quasi-interpolants
zbMATH Keywords: near-best quasi-interpolants
MaRDI profile type: Publication
full work available at URL: j.cam.2009.02.063
OpenAlex ID: W2072568837
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DOI: 10.1016/J.CAM.2009.02.063
description: scientific article; zbMATH DE number 5650064