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<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 loops, e.g. in C:

		new_x = n/2;
		  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


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