<s>
Iteration	B-Algorithm
is	O
the	O
repetition	O
of	O
a	O
process	O
in	O
order	O
to	O
generate	O
a	O
(	O
possibly	O
unbounded	O
)	O
sequence	O
of	O
outcomes	O
.	O
</s>
<s>
Each	O
repetition	O
of	O
the	O
process	O
is	O
a	O
single	O
iteration	B-Algorithm
,	O
and	O
the	O
outcome	O
of	O
each	O
iteration	B-Algorithm
is	O
then	O
the	O
starting	O
point	O
of	O
the	O
next	O
iteration	B-Algorithm
.	O
</s>
<s>
In	O
mathematics	O
and	O
computer	B-General_Concept
science	I-General_Concept
,	O
iteration	B-Algorithm
(	O
along	O
with	O
the	O
related	O
technique	O
of	O
recursion	O
)	O
is	O
a	O
standard	O
element	O
of	O
algorithms	O
.	O
</s>
<s>
In	O
mathematics	O
,	O
iteration	B-Algorithm
may	O
refer	O
to	O
the	O
process	O
of	O
iterating	B-Algorithm
a	I-Algorithm
function	I-Algorithm
,	O
i.e.	O
</s>
<s>
applying	O
a	O
function	O
repeatedly	O
,	O
using	O
the	O
output	O
from	O
one	O
iteration	B-Algorithm
as	O
the	O
input	O
to	O
the	O
next	O
.	O
</s>
<s>
Iteration	B-Algorithm
of	O
apparently	O
simple	O
functions	O
can	O
produce	O
complex	O
behaviors	O
and	O
difficult	O
problems	O
–	O
for	O
examples	O
,	O
see	O
the	O
Collatz	O
conjecture	O
and	O
juggler	O
sequences	O
.	O
</s>
<s>
Another	O
use	O
of	O
iteration	B-Algorithm
in	O
mathematics	O
is	O
in	O
iterative	B-Algorithm
methods	I-Algorithm
which	O
are	O
used	O
to	O
produce	O
approximate	O
numerical	O
solutions	O
to	O
certain	O
mathematical	O
problems	O
.	O
</s>
<s>
Newton	O
's	O
method	O
is	O
an	O
example	O
of	O
an	O
iterative	B-Algorithm
method	I-Algorithm
.	O
</s>
<s>
In	O
computing	O
,	O
iteration	B-Algorithm
is	O
the	O
technique	O
marking	O
out	O
of	O
a	O
block	O
of	O
statements	O
within	O
a	O
computer	B-Application
program	I-Application
for	O
a	O
defined	O
number	O
of	O
repetitions	O
.	O
</s>
<s>
That	O
block	O
of	O
statements	O
is	O
said	O
to	O
be	O
iterated	B-Algorithm
;	O
a	O
computer	O
scientist	O
might	O
also	O
refer	O
to	O
that	O
block	O
of	O
statements	O
as	O
an	O
"	O
iteration	B-Algorithm
"	O
.	O
</s>
<s>
Loops	O
constitute	O
the	O
most	O
common	O
language	O
constructs	O
for	O
performing	O
iterations	B-Algorithm
.	O
</s>
<s>
The	O
following	O
pseudocode	B-Language
"	O
iterates	B-Algorithm
"	O
three	O
times	O
the	O
line	O
of	O
code	O
between	O
the	O
curly	O
brackets	O
through	O
a	O
for	O
loop	O
,	O
and	O
uses	O
the	O
values	O
of	O
i	O
as	O
increments	O
.	O
</s>
<s>
Iterators	O
constitute	O
alternative	O
language	O
constructs	O
to	O
loops	O
,	O
which	O
ensure	O
consistent	O
iterations	B-Algorithm
over	O
specific	O
data	O
structures	O
.	O
</s>
<s>
Iteratees	B-Application
are	O
purely	O
functional	B-Language
language	I-Language
constructs	O
,	O
which	O
accept	O
or	O
reject	O
data	O
during	O
the	O
iterations	B-Algorithm
.	O
</s>
<s>
Recursions	O
and	O
iterations	B-Algorithm
have	O
different	O
algorithmic	O
definitions	O
,	O
even	O
though	O
they	O
can	O
generate	O
identical	O
effects/results	O
.	O
</s>
<s>
The	O
primary	O
difference	O
is	O
that	O
recursion	O
can	O
be	O
employed	O
as	O
a	O
solution	O
without	O
prior	O
knowledge	O
as	O
to	O
how	O
many	O
times	O
the	O
action	O
will	O
have	O
to	O
repeat	O
,	O
while	O
a	O
successful	O
iteration	B-Algorithm
requires	O
that	O
foreknowledge	O
.	O
</s>
<s>
Some	O
types	O
of	O
programming	O
languages	O
,	O
known	O
as	O
functional	B-Language
programming	I-Language
languages	I-Language
,	O
are	O
designed	O
such	O
that	O
they	O
do	O
not	O
set	O
up	O
a	O
block	O
of	O
statements	O
for	O
explicit	O
repetition	O
,	O
as	O
with	O
the	O
for	O
loop	O
.	O
</s>
<s>
The	O
classic	O
example	O
of	O
recursion	O
is	O
in	O
list-sorting	O
algorithms	O
,	O
such	O
as	O
merge	B-Algorithm
sort	I-Algorithm
.	O
</s>
<s>
The	O
merge	B-Algorithm
sort	I-Algorithm
recursive	O
algorithm	O
will	O
first	O
repeatedly	O
divide	O
the	O
list	O
into	O
consecutive	O
pairs	O
;	O
each	O
pair	O
is	O
then	O
ordered	O
,	O
then	O
each	O
consecutive	O
pair	O
of	O
pairs	O
,	O
and	O
so	O
forth	O
until	O
the	O
elements	O
of	O
the	O
list	O
are	O
in	O
the	O
desired	O
order	O
.	O
</s>
<s>
The	O
code	O
below	O
is	O
an	O
example	O
of	O
a	O
recursive	O
algorithm	O
in	O
the	O
Scheme	B-Language
programming	I-Language
language	I-Language
that	O
will	O
output	O
the	O
same	O
result	O
as	O
the	O
pseudocode	B-Language
under	O
the	O
previous	O
heading	O
.	O
</s>
<s>
In	O
some	O
schools	O
of	O
pedagogy	O
,	O
iterations	B-Algorithm
are	O
used	O
to	O
describe	O
the	O
process	O
of	O
teaching	O
or	O
guiding	O
students	O
to	O
repeat	O
experiments	O
,	O
assessments	O
,	O
or	O
projects	O
,	O
until	O
more	O
accurate	O
results	O
are	O
found	O
,	O
or	O
the	O
student	O
has	O
mastered	O
the	O
technical	O
skill	O
.	O
</s>
<s>
In	O
particular	O
,	O
"	O
iterative	B-Algorithm
"	O
is	O
defined	O
as	O
the	O
"	O
process	O
of	O
learning	O
and	O
development	O
that	O
involves	O
cyclical	O
inquiry	O
,	O
enabling	O
multiple	O
opportunities	O
for	O
people	O
to	O
revisit	O
ideas	O
and	O
critically	O
reflect	O
on	O
their	O
implication.	O
"	O
</s>
<s>
Unlike	O
computing	O
and	O
math	O
,	O
educational	O
iterations	B-Algorithm
are	O
not	O
predetermined	O
;	O
instead	O
,	O
the	O
task	O
is	O
repeated	O
until	O
success	O
according	O
to	O
some	O
external	O
criteria	O
(	O
often	O
a	O
test	O
)	O
is	O
achieved	O
.	O
</s>
