Sampling inequalities for sparse grids
type: Item
instance of: scholarly article
title: Sampling inequalities for sparse grids
zbMATH Open document ID: 1416.65058
author: Christian Rieger
author: Holger Wendland
published in: Numerische Mathematik
publication date: 2017-06-09T00:00:00Z
review text: The authors use a construction technique (Smolyak algorithm) to build a multivariate operator on a sparse grid having almost the same convergence properties as the univariate operator from which it was constructed. Polynomial reproductions are used. Then some sampling inequalities for functions from mixed regularity Sobolev spaces on sparse grids are derived. For classical sparse grids built from Chebyshev points, both cases of oversampling and non-oversampling are taken into account. In the end, the derived sampling inequalities are used for obtaining error estimates for stable reconstruction processes as norm-minimal kernel-based interpolation and penalized least-squares approximation in mixed order Sobolev spaces.
reviewed by: Nicoleta Breaz
Mathematics Subject Classification ID: 65D10
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 41A25
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 6728588
zbMATH Keywords: sampling inequalities
zbMATH Keywords: sparse grids
MaRDI profile type: Publication
full work available at URL: s00211-016-0845-7
OpenAlex ID: W2537590198
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DOI: 10.1007/S00211-016-0845-7
description: scientific article; zbMATH DE number 6728588