# 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 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);

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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