Multivariate approximation

Summary

Multivariate approximation is the part of approximation theory that approximates functions of several variables. Its tools include polynomials in several variables, tensor product methods, radial basis functions, box splines, sparse grids and neural networks. Many one-dimensional facts fail or change form here: for instance, interpolation by polynomials at arbitrary distinct points is no longer always possible. A central question is how the error depends on the dimension, which leads to the curse of dimensionality.