Rk. Beatson et Gn. Newsam, FAST EVALUATION OF RADIAL BASIS FUNCTIONS - MOMENT-BASED METHODS, SIAM journal on scientific computing (Print), 19(5), 1998, pp. 1428-1449
This paper presents a new method for the fast evaluation of univariate
radial basis functions of the form s(x) = Sigma(n=1)(n) d(n)phi(\x -
x(n)\) to within accuracy epsilon. The method can be viewed as a gener
alization 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 ph
i. That is, with this method changing to a new phi requires only codin
g a one- or two-line function for the (slow) evaluation of phi. In con
trast, adapting the usual fast multipole method to a new phi involves
much mathematical analysis of appropriate series expansions and corres
ponding translation operators, followed by a substantial amount of wor
k expressing this mathematics in code.