Rapid evaluation of radial basis functions

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:180

Article

Roussos, G ; Baxter, BJC

关键词: radial basis function interpolation;    fast summation;    multiquadric;    thin-plate spline;   

DOI  :  10.1016/j.cam.2004.10.002

来源: Elsevier

【 摘 要 】

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. (c) 2004 Elsevier B.V. All rights reserved.

【 授权许可】

Free