Nonlinear n-Term Approximation

Broadly speaking, nonlinear approximation theory in linear spaces deals with approximation from nonlinear subsets resp. approximation methods not represented by linear operators. While approximation by rational functions, exponential sums, and splines with free knots are by now classical themes, the more recent concept of nonlinear n-term approximation from dictionaries is general enough to directly relate to modern adaptive computational methods and optimal design methods in various application fields and, at the same time, specific enough to allow for some mathematical treatment.

The talk will introduce the basic definitions, give a series of examples (dimension reduction in computational models, coding, wavelet compression), and, time permitting, report some recent results on the worst-case behavior of Greedy algorithms associated with expansions in Banach spaces.