RBF-based tensor decomposition with applications to oenology

IF 0.6 Q3 MATHEMATICS
E. Perracchione
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引用次数: 1

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.
基于rbf的张量分解及其在酿酒学中的应用
正如通常所说的那样,无网格方法可以在任何维度上工作,并且易于实现。然而,在实际应用中,为了在维数增加时保持收敛顺序,它们需要大量的采样点,计算成本和内存都令人望而却步。此外,当涉及大量点时,径向基函数(RBF)近似的通常不稳定性变得明显。为了部分克服这一缺点,我们建议应用张量分解方法。这与理性rbf一起,使我们能够获得高维的有效插值方案。我们的方法的有效性也通过酿酒学的应用得到了验证。
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来源期刊
CiteScore
1.70
自引率
7.70%
发文量
0
审稿时长
8 weeks
期刊介绍: Dolomites Research Notes on Approximation is an open access journal that publishes peer-reviewed papers. It also publishes lecture notes and slides of the tutorials presented at the annual Dolomites Research Weeks and Workshops, which have been organized regularly since 2006 by the Padova-Verona Research Group on Constructive Approximation and Applications (CAA) in Alba di Canazei (Trento, Italy). The journal publishes, on invitation, survey papers and summaries of Ph.D. theses on approximation theory, algorithms, and applications.
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