inverse distance weighting

Inverse distance weighting (IDW) is a simple method for interpolation, a process of assigning values to unknown points by using values from known points. A simple IDW weighting factor is

w(d)=\frac{1}{d^p}

, where

w(d)

is the weighting factor applied to a known value,

d

is the distance from the known value to the unknown value, and

p

is a user-selected power factor. Here weight decreases as distance increases from the interpolated points. Greater values of

p

assign greater influence to values closest to the interpolated point. A general form of interpolating a value using IDW is

Z=\frac{\sum_{n=1}^N \frac{Z_i}{d_i^p}}{\sum_{n=1}^N \frac{1}{d_i^p}}

where

Z

is the value of the interpolated point,

Z_i

is a known value, and

N

is the total number of known points used in interpolation. See also linear interpolation.

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