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Monotonicity preserving approximation of multivariate scattered data
This paper describes a new method of monotone interpolation and smoothing of multivariate scattered data. It is based on the assumption that the function to be approximated is Lipschitz continuous. The method provides the optimal approximation in the worst case scenario and tight error bounds. Smoothing of noisy data subject to monotonicity constraints is converted into a quadratic programming problem. Estimation of the unknown Lipschitz constant from the data by sample splitting and cross-validation is described. Extension of the method for locally Lipschitz functions is presented.
History
Journal
BIT numerical mathematicsVolume
45Issue
4Pagination
653 - 677Publisher
Kluwer Academic PublishersLocation
Dordrecht, The NetherlandsPublisher DOI
ISSN
0006-3835eISSN
1572-9125Language
engNotes
The original publication can be found at www.springerlink.comPublication classification
C1 Refereed article in a scholarly journalCopyright notice
2005, SpringerUsage metrics
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