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?