Closed form representations for a class of compactly supported radial basis functions

Hubbert, Simon (2012) Closed form representations for a class of compactly supported radial basis functions. Advances in Computational Mathematics 36 (1), pp. 115-136. ISSN 1019-7168.

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Abstract

In this paper we re-examine Wendland's strategy for the construction of compactly supported positive denite radial basis functions. We acknowledge that this strategy can be modied to capture a much larger range of functions, in- cluding the so-called missing Wendland functions which have been the subject of a recent paper by Schaback [5]. Our approach is to focus on a general integral representation of such functions and we will show how a careful evaluation of this integral leads to new closed form expressions for both Wendland's original functions and the missing ones. The resulting expressions are easy to code and so provide the potential user with a quick way of accessing a desired example for a given application.

Item Type:	Article
Keyword(s) / Subject(s):	Positive definite functions, Compactly supported radial basis functions, Hypergeometric functions, Associated Legendre functions
School or Research Centre:	Birkbeck Schools and Research Centres > School of Business, Economics & Informatics > Economics, Mathematics and Statistics
Depositing User:	Administrator
Date Deposited:	13 Jan 2011 14:32
Last Modified:	17 Apr 2013 12:33
URI:	http://eprints.bbk.ac.uk/id/eprint/2938

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