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iteration

## iteration

```  3  definitions  found

From  Webster's  Revised  Unabridged  Dictionary  (1913)  [web1913]:

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

What  needs  this  iteration,  woman?  --Shak.

From  WordNet  r  1.6  [wn]:

iteration
n  :  doing  or  saying  again  [syn:  {reiteration}]

From  The  Free  On-line  Dictionary  of  Computing  (13  Mar  01)  [foldoc]:

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)

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