<s>
The	O
fast	B-Algorithm
multipole	I-Algorithm
method	I-Algorithm
(	O
FMM	O
)	O
is	O
a	O
numerical	B-General_Concept
technique	O
that	O
was	O
developed	O
to	O
speed	O
up	O
the	O
calculation	O
of	O
long-ranged	O
forces	O
in	O
the	O
n-body	B-Algorithm
problem	O
.	O
</s>
<s>
The	O
FMM	O
has	O
also	O
been	O
applied	O
in	O
accelerating	O
the	O
iterative	B-Algorithm
solver	I-Algorithm
in	O
the	O
method	B-Algorithm
of	I-Algorithm
moments	I-Algorithm
(	O
MOM	O
)	O
as	O
applied	O
to	O
computational	O
electromagnetics	O
problems	O
.	O
</s>
<s>
If	O
the	O
FMM	O
is	O
then	O
applied	O
in	O
a	O
hierarchical	O
manner	O
,	O
it	O
can	O
improve	O
the	O
complexity	O
of	O
matrix-vector	O
products	O
in	O
an	O
iterative	B-Algorithm
solver	I-Algorithm
from	O
to	O
in	O
finite	O
arithmetic	O
,	O
i.e.	O
,	O
given	O
a	O
tolerance	O
,	O
the	O
matrix-vector	O
product	O
is	O
guaranteed	O
to	O
be	O
within	O
a	O
tolerance	O
The	O
dependence	O
of	O
the	O
complexity	O
on	O
the	O
tolerance	O
is	O
,	O
i.e.	O
,	O
the	O
complexity	O
of	O
FMM	O
is	O
.	O
</s>
