Fast evaluation of radial basis functions: I
نویسندگان
چکیده
منابع مشابه
Fast Evaluation of Radial Basis Functions: Moment-Based Methods
This paper presents a new method for the fast evaluation of univariate radial basis functions of the form s(x) = ∑N n=1 dnφ(|x− xn|) to within accuracy . The method can be viewed as a generalization of the fast multipole method in which calculations with far field expansions are replaced by calculations involving moments of the data. The method has the advantage of being adaptive to changes in ...
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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 b...
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We present a fast multipole algorithm for the evaluation of pairwise interaction through the radial basis functions such as 1/r, ffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2 þ a2 p and 1= ffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2 þ a2 p (with a > 0) in both two and three dimensions. Our algorithm is an extension of the kernel independent fast multipole method presented in Ying et al. [L. Y...
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A generalised multiquadric radial basis function is a function of the form s(x) = ∑N i=1 diφ(|x − ti|), where φ(r) = ( r2 + τ2 )k/2 , x ∈ Rn, and k ∈ Z is odd. The direct evaluation of an N centre generalised multiquadric radial basis function at m points requires O(mN) flops, which is prohibitive when m and N are large. Similar considerations apparently rule out fitting an interpolating N cent...
متن کاملFast Evaluation of Radial Basis Functions: Methods for Four-Dimensional Polyharmonic Splines
As is now well known for some basic functions φ, hierarchical and fast multipole-like methods can greatly reduce the storage and operation counts for fitting and evaluating radial basis functions. In particular, for spline functions of the form
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ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 1992
ISSN: 0898-1221
DOI: 10.1016/0898-1221(92)90167-g