A parallel multivariate interpolation algorithm with radial basis functions

This paper presents an efficient and highly scalable parallel version of the Modified RBF Shepard's method presented in [5]. This method maintains the "metric" nature and the advantages of Shepard's method and, at the same time, improves its accuracy by exploiting the characteristics of flexibility and accuracy which have made the radial basis functions a well-established tool for multivariate interpolation. Due to its locality, this method can be easily and efficiently parallelized on a distributed memory parallel architecture. The performance of the parallel algorithm has been studied theoretically and the experimental results obtained by running its implementation on a Cray T3E parallel machine, using the MPI interface, confirm the theoretical efficiency.