<s>
In	O
mathematics	O
,	O
error	B-Algorithm
analysis	I-Algorithm
is	O
the	O
study	O
of	O
kind	O
and	O
quantity	O
of	O
error	O
,	O
or	O
uncertainty	O
,	O
that	O
may	O
be	O
present	O
in	O
the	O
solution	O
to	O
a	O
problem	O
.	O
</s>
<s>
This	O
issue	O
is	O
particularly	O
prominent	O
in	O
applied	O
areas	O
such	O
as	O
numerical	B-General_Concept
analysis	I-General_Concept
and	O
statistics	O
.	O
</s>
<s>
In	O
numerical	O
simulation	O
or	O
modeling	O
of	O
real	O
systems	O
,	O
error	B-Algorithm
analysis	I-Algorithm
is	O
concerned	O
with	O
the	O
changes	O
in	O
the	O
output	O
of	O
the	O
model	O
as	O
the	O
parameters	O
to	O
the	O
model	O
vary	O
about	O
a	O
mean	O
.	O
</s>
<s>
For	O
instance	O
,	O
in	O
a	O
system	O
modeled	O
as	O
a	O
function	O
of	O
two	O
variables	O
Error	B-Algorithm
analysis	I-Algorithm
deals	O
with	O
the	O
propagation	O
of	O
the	O
numerical	B-Algorithm
errors	I-Algorithm
in	O
and	O
(	O
around	O
mean	O
values	O
and	O
)	O
to	O
error	O
in	O
(	O
around	O
a	O
mean	O
)	O
.	O
</s>
<s>
In	O
numerical	B-General_Concept
analysis	I-General_Concept
,	O
error	B-Algorithm
analysis	I-Algorithm
comprises	O
both	O
forward	O
error	B-Algorithm
analysis	I-Algorithm
and	O
backward	O
error	B-Algorithm
analysis	I-Algorithm
.	O
</s>
<s>
Forward	O
error	B-Algorithm
analysis	I-Algorithm
involves	O
the	O
analysis	O
of	O
a	O
function	O
which	O
is	O
an	O
approximation	O
(	O
usually	O
a	O
finite	O
polynomial	O
)	O
to	O
a	O
function	O
to	O
determine	O
the	O
bounds	O
on	O
the	O
error	O
in	O
the	O
approximation	O
;	O
i.e.	O
,	O
to	O
find	O
such	O
that	O
The	O
evaluation	O
of	O
forward	O
errors	O
is	O
desired	O
in	O
validated	B-Algorithm
numerics	I-Algorithm
.	O
</s>
<s>
Backward	O
error	B-Algorithm
analysis	I-Algorithm
,	O
the	O
theory	O
of	O
which	O
was	O
developed	O
and	O
popularized	O
by	O
James	O
H	O
.	O
Wilkinson	O
,	O
can	O
be	O
used	O
to	O
establish	O
that	O
an	O
algorithm	O
implementing	O
a	O
numerical	O
function	O
is	O
numerically	B-General_Concept
stable	O
.	O
</s>
<s>
Stability	O
is	O
a	O
measure	O
of	O
the	O
sensitivity	O
to	O
rounding	O
errors	O
of	O
a	O
given	O
numerical	O
procedure	O
;	O
by	O
contrast	O
,	O
the	O
condition	B-Algorithm
number	I-Algorithm
of	O
a	O
function	O
for	O
a	O
given	O
problem	O
indicates	O
the	O
inherent	O
sensitivity	O
of	O
the	O
function	O
to	O
small	O
perturbations	O
in	O
its	O
input	O
and	O
is	O
independent	O
of	O
the	O
implementation	O
used	O
to	O
solve	O
the	O
problem	O
.	O
</s>
<s>
We	O
can	O
then	O
use	O
the	O
auto	O
correlation	O
function	O
to	O
estimate	O
the	O
error	B-Application
bar	I-Application
.	O
</s>
<s>
Error	B-Algorithm
analysis	I-Algorithm
alone	O
is	O
typically	O
not	O
sufficient	O
to	O
prove	O
that	O
data	O
have	O
been	O
falsified	O
or	O
fabricated	O
,	O
but	O
it	O
may	O
provide	O
the	O
supporting	O
evidence	O
necessary	O
to	O
confirm	O
suspicions	O
of	O
misconduct	O
.	O
</s>
