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)
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