Year: 2011
Type: conference-paper
Abstract: The purpose of this article is to introduce a kind of data setting to handle radial basis functions.Traditionally the meshless method RBF uses scattered data setting to do interpolations.This approach faces two hard problems.First, the optimal choice of the shape parameters contained in smooth radial functions are not easy to find.Second, the crucial constant ω in the exponential-type error bound, which is O(ω 1 d ), is too large, making this error bound meaningful only when the fill distance d is extremely small.However, in the evenly spaced data setting, an error bound of the form O( √ dω) is established where ω is much sharper than that of the former one.What's important is that whenever this error bound is adopted, the optimal choice of the shape parameter can always be found with the fill distance d of reasonable size.We express the effect of the shape parameter c by explicitly defined functions and present concrete criteria of the optimal choice of c, which do not require too many data points.
DOI: 10.2495/be110231
Author: L. T. Luh
Institution: Providence University
Language: English
Subfield: Mechanics of Materials
Field: Engineering
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2106443924