Extrapolation

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.

Weighted Average

Suppose you have a discrete dataset $I$, with coordinates $X$ on a normed space, and want to map the dataset to another dataset, $O$, with a new set of coordinates $Y$. The operation is performed by constructing mapping coefficients $w$, also called "weights", and by performing a linear combination of the elements of $I$ with the weights, $w$, to compute each element of $O$.

$O_k = \frac{ \sum_i w_{ki} \, I_i }{\sum_i w_{ki}};$

See also

• ConvertToHdf5