Fast Evaluation of Cardinal Radial Basis Interpolants

A cardinal radial basis interpolant S(x), briefly CRBI, is essentially a weighted arithmetic mean of the function values fk (k=1, 2, ...,n), relating to the data points xk of a given set C of a multidimensional Euclidean space. Then S(x) can be rewritten as a proper weighted arithmetic mean of CRBI's Sj(x), (j=1, 2, ...,p), where Sj(x) is quite similar to S(x) but extended only to the jth subset Cj of a partition of C into p parts. The new form of S(x) is particularly suitable for parallel computation with a speedup factor approximately equal to the number of processors involved.