RBF-based tensor decomposition with applications to oenology

Abstract

As usually claimed, meshless methods work in any dimension and are easy to implement. However in practice, to preserve the convergence order when the dimension grows, they need a huge number of sampling points and both computational costs and memory turn out to be prohibitive. Moreover, when a large number of points is involved, the usual instability of the Radial Basis Function (RBF) approximants becomes evident. To partially overcome this drawback, we propose to apply tensor decomposition methods. This, together with rational RBFs, allows us to obtain efficient interpolation schemes for high dimensions. The effectiveness of our approach is also verified by an application to oenology.

Perracchione E. (2020) "RBF-based tensor decomposition with applications to oenology " Dolomites Research Notes on Approximation, 13(1), 36-46. DOI: 10.14658/PUPJ-DRNA-2020-1-5  
Year of Publication
2020
Journal
Dolomites Research Notes on Approximation
Volume
13
Issue Number
1
Start Page
36
Last Page
46
Date Published
05/2020
ISSN Number
2035-6803
Serial Article Number
5
DOI
10.14658/PUPJ-DRNA-2020-1-5
Issue
Section
Articles