[W/K] :: iteration

  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
       n 1: (computer science) a single execution of a set of
            instructions that are to be repeated; "the solution took
            hundreds of iterations" [syn: 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: looping]
       3: doing or saying again; a repeated performance

  36 Moby Thesaurus words for "iteration":
     conduplication, copy, copying, critique, doubling, duplicate,
     duplication, dwelling upon, elaboration, gemination, going over,
     imitation, ingemination, practicing, reaffirmation, recap,
     recapitulation, recital, recountal, recounting, reduplication,
     rehash, rehearsal, reissue, reiteration, repetition, replication,
     reprint, reproduction, restatement, resume, retelling, review,
     summary, summing up, twinning
  
  

  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)