iteration

<programming>

Repetition of a sequence of instructions. A fundamental part of many algorithms. Iteration is characterised by a set of initial conditions, an iterative step and a termination condition.

A well known example of iteration in mathematics is Newton-Raphson iteration. Iteration in programs is expressed using a loop, e.g. in C: 

 new_x = n/2;
 do
 {
   x = new_x;
   new_x = 0.5 * (x + n/x);
 } while (abs(new_x-x) > epsilon);
Iteration can be expressed in functional languages using recursion: 

 solve x n = if abs(new_x-x) > epsilon
 	    then solve new_x n
 	    else new_x
 	    where new_x = 0.5 * (x + n/x)

        solve n/2 n

Last updated: 1998-04-04

Nearby terms:

Iterated Function System ♦ iteration ♦ iterative deepening ♦ iterator

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