Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/26266
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

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