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

    Hubbert, Simon (2012) Closed form representations for a class of compactly supported radial basis function. 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 definite radial basis functions. We acknowledge that this strategy can be modified to capture a much larger range of functions, including the so-called missing Wendland functions which have been the subject of a recent paper by Schaback (Adv Comput Math 34:67–81, 2011). 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.

    Metadata

    Item Type: Article
    Keyword(s) / Subject(s): Positive definite functions, Compactly supported radial basis functions, Hypergeometric functions, Associated Legendre functions
    School: Birkbeck Schools and Departments > School of Business, Economics & Informatics > Economics, Mathematics and Statistics
    Depositing User: Simon Hubbert
    Date Deposited: 01 Oct 2013 10:49
    Last Modified: 27 Jul 2019 13:55
    URI: http://eprints.bbk.ac.uk/id/eprint/8231

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