  The meshless/meshfree radial basis function (RBF) method is a powerful
technique for interpolating scattered data. But, solving large RBF
interpolation problems without fast summation methods is computationally
expensive. For RBF interpolation with $N$ points, using a direct method
requires $\mathcal{O}(N^2)$ operations. As a fast summation method, the fast
multipole method (FMM) has been implemented in speeding up the matrix-vector
multiply, which reduces the complexity from $\mathcal{O}(N^2)$ to
$\mathcal{O}(N^{1.5})$ and even to $\mathcal{O}(NlogN)$ for the multilevel fast
multipole method (MLFMM). In this paper, we present a novel kernel-independent
fast multipole method for RBF interpolation, which is used in combination with
the evaluation of point-to-point interactions by RBF and the fast matrix-vector
multiplication. This approach is based on band-limited approximation and
quadrature rules, which extends the range of applicability of FMM.

Numerical Analysis