Radial basis functions for the multivariate interpolation of large scattered data sets

An efficient method for the multivariate interpolation of very large scattered data sets is presented. It is based on the local use of radial basis functions and represents a further improvement of the well known Shepard's method. Although the latter is simple and well suited for multivariate interpolation, it does not share the good reproduction quality of other methods widely used for bivariate interpolation. On the other hand, radial basis functions, which have proven to be highly useful for multivariate scattered data interpolation, have a severe drawback. They are unable to interpolate large sets in an efficient and numerically stable way and maintain a good level of reproduction quality at the same time. Both problems have been circumvented using radial basis functions to evaluate the nodal function of the modified Shepard's method. This approach exploits the flexibility of the method and improves its reproduction quality. The proposed algorithm has been implemented and numerical results confirm its efficiency.