Fitting multidimensional data using gradient penalties and the sparse grid combination technique
type: Item
instance of: scholarly article
title: Fitting multidimensional data using gradient penalties and the sparse grid combination technique
zbMATH Open document ID: 1166.65004
author: Jochen Garcke
author: Markus Hegland
published in: Computing
publication date: 2009-04-27T00:00:00Z
review text: Sparse grids, combined with gradient penalties provide an attractive tool for regularised least squares fitting. It has earlier been found that the combination technique, which build a sparse grid function using a linear combination of approximations on partial grids, is here not as effective as in the case of elliptic partial differential equations. The authors argue that this is due to the irregular and random data distribution, as well as the proportion of the number of data to the grid resolution. These effects are investigated both theoretically and by experiments.
Mathematics Subject Classification ID: 65C60
Mathematics Subject Classification ID: 62G08
Mathematics Subject Classification ID: 65D10
Mathematics Subject Classification ID: 62J02
zbMATH DE Number: 5547557
zbMATH Keywords: sparse grids
zbMATH Keywords: combination technique
zbMATH Keywords: regression
zbMATH Keywords: high dimensional data
zbMATH Keywords: regularisation
zbMATH Keywords: numerical examples
zbMATH Keywords: least squares fitting
reviewed by: Rózsa Horváth-Bokor
MaRDI profile type: Publication
full work available at URL: s00607-009-0027-x
OpenAlex ID: W2068953972
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DOI: 10.1007/S00607-009-0027-X
description: scientific article; zbMATH DE number 5547557