Extrapolation
From MohidWiki
Extrapolation is often required when interpolation techniques cannot be used while mapping information from one dataset to a grid. Extrapolation methods vary, yielding different results both in quality and in performance. This article proposes a couple of simple extrapolation techniques based that use all the information available to extrapolate. The techniques inspire from the weighted average principle.
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Weighted Average
Suppose you have a discrete dataset , with coordinates on a normed space, and want to map the dataset to another dataset, , with a new set of coordinates . The operation is performed by constructing mapping coefficients , also called "weights", and by performing a linear combination of the elements of with the weights, , to compute each element of .