iteration
    n 1: (computer science) a single execution of a set of
         instructions that are to be repeated; "the solution took
         hundreds of iterations" [syn: iteration, loop]
    2: (computer science) executing the same set of instructions a
       given number of times or until a specified result is
       obtained; "the solution is obtained by iteration" [syn:
       iteration, looping]
    3: doing or saying again; a repeated performance

Iteration \It`er*a"tion\, n. [L. iteratio.]
   1. Recital or performance a second time; repetition. --Bacon.
      [1913 Webster]

            What needs this iteration, woman?     --Shak.
      [1913 Webster]

   2. (Computers) The execution of a statement or series of
      statements in a loop which is repeated in a computer
      program; as, at each iteration, the counter is incremented
      by 2.
      [PJC]

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 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)