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iteration



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 a loop, 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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