Abstract
Barnes interpolation is a method that is widely used in geospatial sciences like meteorology to remodel data values recorded at irregularly distributed points into a representative analytical field. When implemented naively, the computational complexity of Barnes interpolation depends directly on both the number of sample points and the number of grid points. In the era of highly resolved grids and overwhelming numbers of sample points, which originate e.g. from the Internet of Things or from crowd-sourced data, this computation can be quite demanding even on high-performance machines. This paper presents new approaches how very good approximations of Barnes interpolation can be implemented using fast algorithms. Two use cases are in particular considered, namely (1) where the used grid is embedded in the Euclidean plane and (2) where the grid is located on the unit sphere.
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