  The radial basis function (RBF) and quasi Monte Carlo (QMC) methods are two
very promising schemes to handle high-dimension problems with complex and
moving boundary geometry due to the fact that they are independent of
dimensionality and inherently meshless. The two strategies are seemingly
irrelevant and are so far developed independently. The former is largely used
to solve partial differential equations (PDE), neural network, geometry
generation, scattered data processing with mathematical justifications of
interpolation theory [1], while the latter is often employed to evaluate
high-dimension integration with the Monte Carlo method (MCM) background [2].
The purpose of this communication is to try to establish their intrinsic
relationship on the grounds of numerical integral. The kernel function of
integral equation is found the key to construct efficient RBFs. Some
significant results on RBF construction, error bound and node placement are
also presented. It is stressed that the RBF is here established on integral
analysis rather than on the sophisticated interpolation and native space
analysis.
