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);
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
(1998-04-04)