Editing Inverse distance weighting (section)

==Definition of the problem==
The expected result is a discrete assignment of the unknown function <math>u</math> in a study region:

:<math>u(x): x \to \mathbb{R}, \quad x \in \mathbf{D} \sub \mathbb{R}^n,</math>

where <math>\mathbf{D}</math> is the study region.

The set of <math>N</math> known data points can be described as a list of [[tuple]]s:

:<math>[(x_1, u_1), (x_2, u_2), ..., (x_N, u_N)].</math>

The function is to be "smooth" (continuous and once differentiable), to be exact (<math>u(x_i) = u_i</math>) 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 computing|parallel resources]]).