Computable Analysis

Computable Analysis studies those functions on the real numbers and related sets which can be computed by machines such as digital computers. It connects two traditionally disjoint fields, namely Analysis/Numerical Analysis on the one hand and Computability/Computational Complexity on the other hand, combining concepts of approximation and of computation. In particular, Computable Analysis supplies an algorithmic foundation of numerical computation. While essentially all computablity models for number functions are equivalent (Church’s Thesis) several non-equivalent mathematical models for real number computation are still being discussed.