Inverse distance weighting

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Inverse distance weighting (IDW) is a method for multivariate interpolation, a process of assigning values to unknown points by using values from known points. A simple IDW weighting function, as defined by Shepard[1], 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 positive real number, called the power parameter. Here weight decreases as distance increases from the interpolated points. Greater values of p assign greater influence to values closest to the interpolated point. The most common value of p is 2.

A general form of interpolating a value using IDW is:

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

where Z is the value of the interpolated point, Zi is a known value, and N is the total number of known points used in interpolation.

[edit] References

  1. ^ Shepard, Donald (1968). "A two-dimensional interpolation function for irregularly-spaced data". Proceedings of the 1968 ACM National Conference: 517–524. Retrieved on 2007-02-18. 

[edit] See also

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