<s>
Loosely	O
speaking	O
,	O
a	O
residual	B-Algorithm
is	O
the	O
error	O
in	O
a	O
result	O
.	O
</s>
<s>
that	O
is	O
,	O
"	O
what	O
is	O
left	O
of	O
the	O
right	O
hand	O
side	O
"	O
after	O
subtracting	O
f(x0 )	O
"	O
(	O
thus	O
,	O
the	O
name	O
"	O
residual	B-Algorithm
"	O
:	O
what	O
is	O
left	O
,	O
the	O
rest	O
)	O
.	O
</s>
<s>
If	O
the	O
exact	O
value	O
of	O
x	O
is	O
not	O
known	O
,	O
the	O
residual	B-Algorithm
can	O
be	O
computed	O
,	O
whereas	O
the	O
error	O
cannot	O
.	O
</s>
<s>
Similar	O
terminology	O
is	O
used	O
dealing	O
with	O
differential	O
,	O
integral	B-Algorithm
and	O
functional	O
equations	O
.	O
</s>
<s>
over	O
the	O
domain	O
,	O
where	O
the	O
function	O
is	O
expected	O
to	O
approximate	O
the	O
solution	O
,	O
or	O
some	O
integral	B-Algorithm
of	O
a	O
function	O
of	O
the	O
difference	O
,	O
for	O
example	O
:	O
</s>
<s>
In	O
many	O
cases	O
,	O
the	O
smallness	O
of	O
the	O
residual	B-Algorithm
means	O
that	O
the	O
approximation	O
is	O
close	O
to	O
the	O
solution	O
,	O
i.e.	O
,	O
</s>
<s>
In	O
these	O
cases	O
,	O
the	O
initial	O
equation	O
is	O
considered	O
as	O
well-posed	B-Algorithm
;	O
and	O
the	O
residual	B-Algorithm
can	O
be	O
considered	O
as	O
a	O
measure	O
of	O
deviation	O
of	O
the	O
approximation	O
from	O
the	O
exact	O
solution	O
.	O
</s>
<s>
When	O
one	O
does	O
not	O
know	O
the	O
exact	O
solution	O
,	O
one	O
may	O
look	O
for	O
the	O
approximation	O
with	O
small	O
residual	B-Algorithm
.	O
</s>
<s>
Residuals	B-Algorithm
appear	O
in	O
many	O
areas	O
in	O
mathematics	O
,	O
including	O
iterative	B-Algorithm
solvers	I-Algorithm
such	O
as	O
the	O
generalized	O
minimal	O
residual	B-Algorithm
method	O
,	O
which	O
seeks	O
solutions	O
to	O
equations	O
by	O
systematically	O
minimizing	O
the	O
residual	B-Algorithm
.	O
</s>
