Nonlinear approximation

Summary

Nonlinear approximation approximates a function by elements of a set that is not a linear space. A typical such set is the sums of $n$ terms chosen freely from a dictionary. The approximant may adapt to the function, for example by placing spline knots or wavelets where the function is rough. Typical cases are n-term approximation, rational approximation, splines with free knots and neural networks. For functions with isolated singularities it can be much more efficient than linear approximation with the same number of parameters.