Shepard interpolation algorithm
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Classic way to get a value based on other points in Shepard (Inverse distance weighting) method: $$F(x,y) = Sigma_{k=1}^{N}w_{k}(x,y)f_{k} / Sigma_{k=1}^{N}w_{k}(x,y) $$ where $w$ can be compute as some expression with metric (euclidian for example). The paper Scattered Data Interpolation: Tests of Some Methods by Franke tells (p.5) that another way to get needed value is compute follows: $$F(x,y) = Sigma_{k=1}^{N}w_{k} [f_{k} + frac{partial f}{partial x}_{k}(x-x_{k}) + frac{partial f}{partial y}_{k}(y-y_{k})]/ Sigma_{k=1}^{N}w_{k}(x,y)$$ But I do not understand, how can I coumpute this. For example I have sample: $$mathbf{x} = [0, 2, 4] \ mathbf{y} = [3, 6, 5] $$ and I need to get interpolated value for point $a = 1$ . How can I do this?
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