<s>
In	O
numerical	B-General_Concept
analysis	I-General_Concept
,	O
computational	B-Algorithm
physics	I-Algorithm
,	O
and	O
simulation	O
,	O
discretization	B-Algorithm
error	I-Algorithm
is	O
the	O
error	O
resulting	O
from	O
the	O
fact	O
that	O
a	O
function	O
of	O
a	O
continuous	O
variable	O
is	O
represented	O
in	O
the	O
computer	O
by	O
a	O
finite	O
number	O
of	O
evaluations	O
,	O
for	O
example	O
,	O
on	O
a	O
lattice	B-Algorithm
.	O
</s>
<s>
Discretization	B-Algorithm
error	I-Algorithm
can	O
usually	O
be	O
reduced	O
by	O
using	O
a	O
more	O
finely	O
spaced	O
lattice	B-Algorithm
,	O
with	O
an	O
increased	O
computational	O
cost	O
.	O
</s>
<s>
Discretization	B-Algorithm
error	I-Algorithm
is	O
the	O
principal	O
source	O
of	O
error	O
in	O
methods	O
of	O
finite	B-Algorithm
differences	I-Algorithm
and	O
the	O
pseudo-spectral	B-Algorithm
method	I-Algorithm
of	O
computational	B-Algorithm
physics	I-Algorithm
.	O
</s>
<s>
When	O
we	O
define	O
the	O
derivative	O
of	O
as	O
or	O
,	O
where	O
is	O
a	O
finitely	O
small	O
number	O
,	O
the	O
difference	O
between	O
the	O
first	O
formula	O
and	O
this	O
approximation	O
is	O
known	O
as	O
discretization	B-Algorithm
error	I-Algorithm
.	O
</s>
<s>
In	O
signal	O
processing	O
,	O
the	O
analog	O
of	O
discretization	B-Algorithm
is	O
sampling	B-Algorithm
,	O
and	O
results	O
in	O
no	O
loss	O
if	O
the	O
conditions	O
of	O
the	O
sampling	B-Algorithm
theorem	O
are	O
satisfied	O
,	O
otherwise	O
the	O
resulting	O
error	O
is	O
called	O
aliasing	B-Error_Name
.	O
</s>
<s>
Discretization	B-Algorithm
error	I-Algorithm
,	O
which	O
arises	O
from	O
finite	O
resolution	O
in	O
the	O
domain	O
,	O
should	O
not	O
be	O
confused	O
with	O
quantization	O
error	O
,	O
which	O
is	O
finite	O
resolution	O
in	O
the	O
range	O
(	O
values	O
)	O
,	O
nor	O
in	O
round-off	B-Algorithm
error	I-Algorithm
arising	O
from	O
floating-point	B-Algorithm
arithmetic	I-Algorithm
.	O
</s>
<s>
Discretization	B-Algorithm
error	I-Algorithm
would	O
occur	O
even	O
if	O
it	O
were	O
possible	O
to	O
represent	O
the	O
values	O
exactly	O
and	O
use	O
exact	O
arithmetic	O
–	O
it	O
is	O
the	O
error	O
from	O
representing	O
a	O
function	O
by	O
its	O
values	O
at	O
a	O
discrete	O
set	O
of	O
points	O
,	O
not	O
an	O
error	O
in	O
these	O
values	O
.	O
</s>
