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Inverse distance weighting
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Inverse distance weighting : ウィキペディア英語版
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.
==Definition of the Problem==
The expected result is a discrete assignment of the unknown function u in a study region:
u(x): x \rightarrow \mathbb, \quad x \in \mathbf \sub \mathbb^n
where \mathbf is the study region.
The set of N known data points can be described as a list of tuples:
(u_1), (x_2, u_2), ..., (x_N, u_N) )
The function is to be "smooth" (continuous and once differentiable), to be exact (u(x_i)=u_i) and to meet the user's intuitive expectations about the phenomenon under investigation. Furthermore, the function should be suitable for a computer application at a reasonable cost (nowadays, a basic implementation will probably make use of parallel resources).

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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