A low cost and highly accurate technique for big data spatial-temporal interpolation
Multivariate approximation and interpolation, for instance with radial basis functions, is a fruitful approach to the handling of big data. In contrast to approximation by polynomials or even piecewise polynomials -- splines -- the radial basis function approach usually provides higher accuracy, more stability and low computational cost. It is in particular available for scattered data in any dimension, too. On top of this, any number of data can be dealt with, so this is an excellent approach to big data. In this article, the computational efficiency is improved further by computing the approximations to big data with a layered algorithm, where at each layer, a relatively small linear system of equations must be solved in order to compute the approximation. The well-known and very useful multiquadrics radial basis function \(\phi(r)=\sqrt{r^2+c^2}\) with the radius \(r\) and a parameter \(c\) is employed as the (radial basis) kernel function. As a numerical example the air pollution in the US is studied computationally.
scientific article; zbMATH DE number 7188159