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

(1998-04-04)