Analytic Machines and Computability of Analytic Functions

For the definition of computable real und complex functions, the machine model of analytic machines is used. This is a register machine model that allows exact arithmetic and admits infinite converging computations. Results about properties of computable functions are presented.
The model is then applied to give a notion of computable complex-analytic (i.e., holomorphic) functions. The resulting class of functions is shown to have good natural properties, such as closure under composition, local inversion, and analytic continuation.