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Title: Adaptive radial basis function interpolation using an error indicator
Authors: Zhang, Qi
Zhao, Yangzhang
Levesley, Jeremy
First Published: 26-Jan-2017
Publisher: Springer Verlag
Citation: Numerical Algorithms, 2017, in press
Abstract: In some approximation problems, sampling from the target function can be both expensive and time-consuming. It would be convenient to have a method for indicating where approximation quality is poor, so that generation of new data provides the user with greater accuracy where needed. In this paper, we propose a new adaptive algorithm for radial basis function (RBF) interpolation which aims to assess the local approximation quality, and add or remove points as required to improve the error in the specified region. For Gaussian and multiquadric approximation, we have the flexibility of a shape parameter which we can use to keep the condition number of interpolation matrix at a moderate size. Numerical results for test functions which appear in the literature are given for dimensions 1 and 2, to show that our method performs well. We also give a three-dimensional example from the finance world, since we would like to advertise RBF techniques as useful tools for approximation in the high-dimensional settings one often meets in finance.
DOI Link: 10.1007/s11075-017-0265-5
ISSN: 1017-1398
eISSN: 1572-9265
Version: Publisher Version
Status: Peer-reviewed
Type: Journal Article
Rights: Copyright © the authors, 2017. This is an open-access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Appears in Collections:Published Articles, Dept. of Mathematics

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