Iterative procedures

Iterative procedures have many advantages for computation, for instance an approximation to the final answer is provided even if the computation stops abruptly. A model for iterative computation is proposed where a procedure G executed repeatedly "converges" to a function f. A notion of approximation of functions on the integers is used based on limits of densities. Some results on the power of iteration and iterative extensions are obtained. The relation between iteration and composition is investigated. Heuristic procedures are defined. Many interesting problems remain open. The area is very interesting, since a combination of tools from Analysis and Automata theory can be used.