Information-Based Nonlinear Approximation: An Average Case Setting

Nonlinear approximation has usually been studied under deterministic assumption and complete information about the underlying functions. We assume only partial information and we are interested in the average case error and complexity of approximation. It turns out that the problem can be essentially split into two independent problems related to average case nonlinear (restricted) approximation from complete information, and average case unrestricted approximation from partial information. The results are then applied to average case piecewise polynomial approximation, and to average case approximation of real sequences