Multivariate interpolation

Summary

Multivariate interpolation is the construction of a function of several variables that takes given values at given points of $\R^d$ with $d \ge 2$. In one variable, polynomials of degree at most $n$ always interpolate uniquely at $n + 1$ distinct points. In several variables, this depends on the position of the points, see unisolvent point set. For gridded data one uses tensor products of one-dimensional methods, such as bilinear and bicubic interpolation. For scattered data one uses methods adapted to the points, such as radial basis function interpolation, inverse distance weighting, moving least squares and kriging.