article

Theoretical and computational aspects of multivariate interpolation with increasingly flat radial basis functions

Authors:

B. FornbergAuthors Info & Claims

Computers & Mathematics with Applications, Volume 49, Issue 1

Pages 103 - 130

https://doi.org/10.1016/j.camwa.2005.01.010

Published: 01 January 2005 Publication History

Abstract

Multivariate interpolation of smooth data using smooth radial basis functions is considered. The behavior of the interpolants in the limit of nearly flat radial basis functions is studied both theoretically and numerically. Explicit criteria for different types of limits are given. Using the results for the limits, the dependence of the error on the shape parameter of the radial basis function is investigated. The mechanisms that determine the optimal shape parameter value are studied and explained through approximate expansions of the interpolation error.

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Published: 01 January 2005

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https://dl.acm.org/doi/10.1007/s10915-024-02472-x
Glaubitz JNordström JÖffner P(2024)Energy-Stable Global Radial Basis Function Methods on Summation-By-Parts FormJournal of Scientific Computing10.1007/s10915-023-02427-898:1Online publication date: 2-Jan-2024
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