Kriging with moving neighborhoods

Figure 2.4: Example of interpolation with moving neighborhood

Generally the experimental variogram is most accurate for small values of $h$, with uncertainties growing rapidly when $h$ is large. The influence of this problem may be decreased by using moving neighborhoods. With this variant, only the points that lie within a prefixed radios $R$ from point $x_0$ are considered, provided that we are left with an adequate number of data (Fig. 2.4). The redius $R$ is selected so that the lag $h$ will remain with the range of maximum certainty for $\gamma(h)$.

This approach leads also to high saving in the computational cost of the procedure because each linear system is now much smaller (Gaussian elimination has a computational cost proportional to $n^3$, where $n$ is the number of equations).