<s>
In	O
numerical	B-General_Concept
analysis	I-General_Concept
,	O
a	O
numerical	B-Algorithm
method	I-Algorithm
is	O
a	O
mathematical	O
tool	O
designed	O
to	O
solve	O
numerical	O
problems	O
.	O
</s>
<s>
The	O
implementation	O
of	O
a	O
numerical	B-Algorithm
method	I-Algorithm
with	O
an	O
appropriate	O
convergence	O
check	O
in	O
a	O
programming	O
language	O
is	O
called	O
a	O
numerical	B-General_Concept
algorithm	I-General_Concept
.	O
</s>
<s>
Let	O
be	O
a	O
well-posed	B-Algorithm
problem	I-Algorithm
,	O
i.e.	O
</s>
<s>
The	O
problems	O
of	O
which	O
the	O
method	O
consists	O
need	O
not	O
be	O
well-posed	B-Algorithm
.	O
</s>
<s>
If	O
they	O
are	O
,	O
the	O
method	O
is	O
said	O
to	O
be	O
stable	O
or	O
well-posed	B-Algorithm
.	O
</s>
<s>
Necessary	O
conditions	O
for	O
a	O
numerical	B-Algorithm
method	I-Algorithm
to	O
effectively	O
approximate	O
are	O
that	O
and	O
that	O
behaves	O
like	O
when	O
.	O
</s>
<s>
So	O
,	O
a	O
numerical	B-Algorithm
method	I-Algorithm
is	O
called	O
consistent	O
if	O
and	O
only	O
if	O
the	O
sequence	O
of	O
functions	O
pointwise	O
converges	O
to	O
on	O
the	O
set	O
of	O
its	O
solutions	O
:	O
</s>
