File(s) not publicly available
Local polynomial reproduction and moving least squares approximation
journal contribution
posted on 2023-06-07, 21:25 authored by Holger WendlandLocal polynomial reproduction is a key ingredient in providing error estimates for several approximation methods. To bound the Lebesgue constants is a hard task especially in a multivariate setting. We provide a result which allows us to bound the Lebesgue constants uniformly and independently of the space dimension by oversampling. We get explicit and small bounds for the Lebesgue constants. Moreover, we use these results to establish error estimates for the moving least squares approximation scheme, also with special emphasis on the involved constants. We discuss the numerical treatment of the method and analyse its effort. Finally, we give large scale examples.
History
Publication status
- Published
Journal
IMA Journal of Numerical AnalysisISSN
0272-4979Publisher
Oxford University PressExternal DOI
Issue
1Volume
21Page range
285-300Department affiliated with
- Mathematics Publications
Full text available
- No
Peer reviewed?
- Yes
Legacy Posted Date
2012-02-06Usage metrics
Categories
No categories selectedKeywords
Licence
Exports
RefWorks
BibTeX
Ref. manager
Endnote
DataCite
NLM
DC