Multivariate interpolation

In numerical analysis, multivariate interpolation or multidimensional interpolation is interpolation on multivariate functions, having more than one variable or defined over a multi-dimensional domain.^[1] A common special case is bivariate interpolation or two-dimensional interpolation, based on two variables or two dimensions. When the variates are spatial coordinates, it is also known as spatial interpolation.

The function to be interpolated is known at given points ${\displaystyle (x_{i},y_{i},z_{i},\dots )}$ and the interpolation problem consists of yielding values at arbitrary points ${\displaystyle (x,y,z,\dots )}$.

Multivariate interpolation is particularly important in geostatistics, where it is used to create a digital elevation model from a set of points on the Earth's surface (for example, spot heights in a topographic survey or depths in a hydrographic survey).