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Rapid evaluation of radial basis functions

Roussos, George and Baxter, Brad J.C. (2005) Rapid evaluation of radial basis functions. Journal of Computational and Applied Mathematics 180 (1), pp. 51-70. ISSN 0377-0427.


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Over the past decade, the radial basis function method has been shown to produce high quality solutions to the multivariate scattered data interpolation problem. However, this method has been associated with very high computational cost, as compared to alternative methods such as finite element or multivariate spline interpolation. For example. the direct evaluation at M locations of a radial basis function interpolant with N centres requires O(M N) floating-point operations. In this paper we introduce a fast evaluation method based on the Fast Gauss Transform and suitable quadrature rules. This method has been applied to the Hardy multiquadric, the inverse multiquadric and the thin-plate spline to reduce the computational complexity of the interpolant evaluation to O(M + N) floating point operations. By using certain localisation properties of conditionally negative definite functions this method has several performance advantages against traditional hierarchical rapid summation methods which we discuss in detail.

Item Type: Article
Keyword(s) / Subject(s): radial basis function interpolation, fast summation, multiquadric, thin-plate spline, fast gauss transform, scattered data, interpolation
School or Research Centre: Birkbeck Schools and Research Centres > School of Business, Economics & Informatics > Computer Science and Information Systems
Depositing User: Sandra Plummer
Date Deposited: 01 Feb 2006
Last Modified: 17 Apr 2013 12:32

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