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 * 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