Fast Evaluation of Radial Basis Functions: Moment-Based Methods

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 ...

Fast Evaluation of Radial Basis Functions: Methods for Generalized Multiquadrics in Rn

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...

Fast 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

THE COMPARISON OF EFFICIENT RADIAL BASIS FUNCTIONS COLLOCATION METHODS FOR NUMERICAL SOLUTION OF THE PARABOLIC PDE’S

In this paper, we apply the compare the collocation methods of meshfree RBF over differential equation containing partial derivation of one dimension time dependent with a compound boundary nonlocal condition.

Fast Evaluation of Radial Basis Fun tions: Methods Based on Partition of Unity