A numerical algorithm for multidimensional modeling of scattered data points

Abstract

In this paper we propose an N-dimensional (Nd) algorithm for surface modeling of multivariate scattered data points. This code is implemented in MATLAB environment to numerically approximate (usually) large data point sets in $$\mathbb {R}^N$$ , for any $$N \in \mathbb {N}$$ . Since we need to organize the points in a Nd space, we build a kd-tree space-partitioning data structure, which is used to efficiently apply a partition of unity interpolant. This global method is combined with local radial basis function approximants and compactly supported weight functions. A detailed design of the partition of unity algorithm and a complexity analysis of the computational procedures are also considered. Finally, in several numerical experiments we show the performances, i.e., accuracy, efficiency and stability, of the Nd interpolation algorithm, considering various sets of Halton data points for $$N \le 5$$ .