How do local interpolation methods differ from global ones in terms of data usage?

Local interpolation methods differ from global ones by using only a small subset

n

of the total

m

available data points to compute the value at a specific grid point. Global methods, by contrast, typically use all

m

data points to construct a single continuous function for the entire domain. Local methods are computationally efficient for large datasets and directly apply the locality condition.

Conditions

The method is a local interpolation technique.
The total number of available data points is $m$ .
The number of points in the local subset is $n$ , where $n < m$ .

Reasoning, step by step

Identify the total number of available data points $m$ .
For a specific target grid point, select a small subset $n$ of nearby data points.
Compute the interpolated value at the grid point using only this subset $n$ .
Repeat this local computation for other grid points across the domain.

Example

The slide states that for local interpolation, “Only a small subset n of the total m points is used,” and lists methods like Voronoi polygons, TIN, and IDW as examples of local approaches.

Common misconceptions

Assuming that local interpolation methods require processing the entire dataset for every single grid point.
Believing that global and local methods use the exact same number of data points for a single evaluation.

Watch the explanation

YouTubeInterpolation principles lecture (NCSU Geospatial Modeling and Analysis)

11:28 – 12:06Watch this moment ↗

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Answers are generated from source material and independently checked. Consult the original video or creator if something is unclear.