iteration

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;
 	do
 	{
 	  x = new_x;
 	  new_x = 0.5 * (x + n/x);
 	} while (abs(new_x-x) > epsilon);

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