RBF-based tensor decomposition with applications to oenology

TitleRBF-based tensor decomposition with applications to oenology
Publication TypeJournal
Year of Publication2020
AuthorsPerracchione, E
JournalDolomites Research Notes on Approximation
Date Published05/2020
PublisherPadova University Press
Place PublishedPadova, IT
ISSN Number20356803

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.