This paper describes a new computational approach to multivariate scattered data interpolation. It is assumed that the data is generated by a Lipschitz continuous function f. The proposed approach uses the central interpolation scheme, which produces an optimal interpolant in the worst case scenario. It provides best uniform error bounds on f, and thus translates into reliable learning of f. This paper develops a computationally efficient algorithm for evaluating the interpolant in the multivariate case. We compare the proposed method with the radial basis functions and natural neighbor interpolation, provide the details of the algorithm and illustrate it on numerical experiments. The efficiency of this method surpasses alternative interpolation methods for scattered data.
This nis a post-peer reviewed electronic version of an article published in the Journal of Computational and Applied Mathematics. A link to the published version is provided below.
Field of Research
010301 Numerical Analysis
Socio Economic Objective
970101 Expanding Knowledge in the Mathematical Sciences