The combination technique and some generalisations

Hegland, Markus, Garcke, Jochen and Challis, Vivien (2007) The combination technique and some generalisations. Linear Algebra and Its Applications, 420 2-3: 249-275. doi:10.1016/j.laa.2006.07.014

Author Hegland, Markus
Garcke, Jochen
Challis, Vivien
Title The combination technique and some generalisations
Journal name Linear Algebra and Its Applications   Check publisher's open access policy
ISSN 0024-3795
Publication date 2007
Sub-type Article (original research)
DOI 10.1016/j.laa.2006.07.014
Volume 420
Issue 2-3
Start page 249
End page 275
Total pages 27
Place of publication Philadelphia, United States
Publisher Elsevier
Language eng
Abstract The combination technique has repeatedly been shown to be an effective tool for the approximation with sparse grid spaces. Little is known about the reasons of this effectiveness and in some cases the combination technique can even break down. It is known, however, that the combination technique produces an exact result in the case of a projection into a sparse grid space if the involved partial projections commute. The performance of the combination technique is analysed using a projection framework and the C/S decomposition. Error bounds are given in terms of angles between the spanning subspaces or the projections onto these subspaces. Based on this analysis modified combination coefficients are derived which are optimal in a certain sense and which can substantially extend the applicability and performance of the combination technique.
Keyword Sparse grids
High-dimensional approximation
Linear combination of projections
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
Version Filter Type
Citation counts: TR Web of Science Citation Count  Cited 28 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 43 times in Scopus Article | Citations
Google Scholar Search Google Scholar
Created: Mon, 18 Feb 2008, 15:56:46 EST