Radial basis functions for the multivariate interpolation of large scattered data sets
The authors present an improved version of \textit{D. Shepard}'s radial basis function (RBF) method [A two-dimensional interpolation function for irregularly spaced data, Proceeding of rthe 23rd National Conference, ACM, 517-523 (1968)] using a local interpolation, i.e. compactly supported RBF as nodal functions. This provides the efficiency and reproduction quality and also optimizes the implementation of the multivariate interpolation software of large (several thousand points) scattered data sets given by \textit{R. J. Renka} [ACM Trans. Math. Softw. 14, 149-150 (1988; Zbl 0709.65504); ibid. 14, 151-152 (1988; Zbl 0709.65502)]. The numerical tests for bi-variate and tri-variate interpolation show that the localisation of RBF outperforms the multilevel method in the case, when the number of samples is large.
scientific article; zbMATH DE number 1758445
scientific article