Reconstructing Multivariate Functions from Large Data Sets
In this paper we discuss an efficient method for reconstructing multivariate functions from large sets of scattered data. Our method is based on (conditionally) positive definite kernels and a partition of unity. It is tailored to solve such reconstruction problems efficiently even if the space dimension is high and the number of data points is huge. We generalize the classical interpolation approach to dealing with other information than point evaluations. Finally, we demonstrate the generality of our approach by providing three different examples.
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