Reconstruct multiscale functions using different RBFs in different subdomains (Q2381394)

The author provides a new method for the reconstruction of a multivariate function from a scattered data set by using different radial basis functions (RBFs) and different densities of collocation points in different subdomains. He proves that the linear algebra equations obtained by this interpolation method are solvable and provides some numerical results which show the accuracy and efficiency of the method and prove that this method allows the reconstruction of multiscale functions accurately with relatively few points and so avoids the ill-conditioned problems.