<s>
In	O
mathematics	O
,	O
the	O
additive	B-Algorithm
Schwarz	I-Algorithm
method	I-Algorithm
,	O
named	O
after	O
Hermann	O
Schwarz	O
,	O
solves	O
a	O
boundary	O
value	O
problem	O
for	O
a	O
partial	O
differential	O
equation	O
approximately	O
by	O
splitting	O
it	O
into	O
boundary	O
value	O
problems	O
on	O
smaller	O
domains	O
and	O
adding	O
the	O
results	O
.	O
</s>
<s>
The	O
goal	O
of	O
the	O
computer	B-Application
program	I-Application
would	O
be	O
to	O
calculate	O
the	O
value	O
of	O
f	O
at	O
those	O
64	O
points	O
,	O
which	O
seems	O
easier	O
than	O
finding	O
an	O
abstract	O
function	O
of	O
the	O
square	O
.	O
</s>
<s>
To	O
overcome	O
this	O
,	O
one	O
uses	O
some	O
sort	O
of	O
numerical	O
approximation	O
of	O
the	O
derivatives	O
,	O
see	O
for	O
instance	O
the	O
finite	B-Application
element	I-Application
method	I-Application
or	O
finite	B-Algorithm
differences	I-Algorithm
.	O
</s>
<s>
Which	O
brings	O
us	O
to	O
domain	B-Algorithm
decomposition	I-Algorithm
methods	I-Algorithm
.	O
</s>
<s>
This	O
means	O
that	O
a	O
computer	B-Application
program	I-Application
will	O
have	O
an	O
easier	O
time	O
solving	O
two	O
1×1	O
systems	O
than	O
solving	O
a	O
single	O
2×2	O
system	O
,	O
because	O
the	O
pair	O
of	O
1×1	O
systems	O
are	O
simpler	O
than	O
the	O
single	O
2×2	O
system	O
.	O
</s>
<s>
For	O
instance	O
,	O
we	O
could	O
use	O
four	O
16×16	O
problems	O
,	O
and	O
there	O
's	O
a	O
chance	O
that	O
solving	O
these	O
will	O
be	O
better	O
than	O
solving	O
a	O
single	O
64×64	O
problem	O
even	O
if	O
the	O
domain	B-Algorithm
decomposition	I-Algorithm
algorithm	O
needs	O
to	O
iterate	O
a	O
few	O
times	O
.	O
</s>
