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Title: | A generalization of inverse distance weighting and an equivalence relationship to noise-free Gaussian process interpolation via Riesz representation theorem | Authors: | De Mulder, Wim MOLENBERGHS, Geert VERBEKE, Geert |
Issue Date: | 2018 | Source: | LINEAR & MULTILINEAR ALGEBRA, 66(5), p. 1054-1066 | Abstract: | In this paper, we show the relationship between two seemingly unrelated approximation techniques. On the one hand, a certain class of Gaussian process-based interpolation methods, and on the other hand inverse distance weighting, which has been developed in the context of spatial analysis where there is often a need for interpolating from irregularly spaced data to produce a continuous surface. We develop a generalization of inverse distance weighting and show that it is equivalent to the approximation provided by the class of Gaussian process-based interpolation methods. The equivalence is established via an elegant application of Riesz representation theorem concerning the dual of a Hilbert space. It is thus demonstrated how a classical theorem in linear algebra connects two disparate domains. | Notes: | De Mulder, W (reprint author), Katholieke Univ Leuven, BioStat 1, Leuven, Belgium, wim.demulder@cs.kuleuven.be | Keywords: | Riesz representation theorem; Gaussian process; inverse distance weighting; interpolation; kriging | Document URI: | http://hdl.handle.net/1942/26266 | ISSN: | 0308-1087 | e-ISSN: | 1563-5139 | DOI: | 10.1080/03081087.2017.1337057 | ISI #: | 000427736600015 | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2019 |
Appears in Collections: | Research publications |
Files in This Item:
File | Description | Size | Format | |
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10.1080@03081087.2017.1337057.pdf Restricted Access | Published version | 1.29 MB | Adobe PDF | View/Open Request a copy |
paper_LinearAlgebra_revision.pdf | Peer-reviewed author version | 277.59 kB | Adobe PDF | View/Open |
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