WIT Press


A Simple Remark On The Order Of Approximation By Compactly Supported Radial Basis Functions, And Related Networks

Price

Free (open access)

Paper DOI

10.2495/BT990311

Volume

23

Pages

9

Published

1999

Size

663 kb

Author(s)

Xin Li

Abstract

We consider simultaneous approximation of multivariate functions and their derivatives by using Wendland's compactly supported radial basis functions s,k' By applying a greedy algorithm, it is presented that, regardless of dimension, an O(ra~*/^) order of approximation can be achieved by a linear combination of m translates of s,k- A similar result on approximation by neural networks is established by using univariate radial functions as the activation functions of the networks. 1. Introduction Multivariate interpolation by radial basis functions has been studied and applied in several areas of mathematics, such as approximation theory (cf. Franke^, Micchelli**, Schaback**), curve and surface fitting (cf. Daehlen, Lyche, and Schumaker*), and numerical soluti

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