Inverse distance weighting

Inverse Distance Weighting (IDW) is a type of deterministic method for multivariate interpolation with a known scattered set of points. The assigned values to unknown points are calculated with a weighted average of the values available at the known points.

The name given to this type of methods was motivated by the weighted average applied, since it resorts to the inverse of the distance to each known point ("amount of proximity") when assigning weights.

The expected result is a discrete assignment of the unknown function ${\displaystyle u}$ in a study region:

${\displaystyle u(x):x\rightarrow \mathbb {R} ,\quad x\in \mathbf {D} \subset \mathbb {R} ^{n}}$

where ${\displaystyle \mathbf {D} }$ is the study region.

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