<s>
Toom	O
–	O
Cook	O
,	O
sometimes	O
known	O
as	O
Toom-3	O
,	O
named	O
after	O
Andrei	O
Toom	O
,	O
who	O
introduced	O
the	O
new	O
algorithm	O
with	O
its	O
low	O
complexity	O
,	O
and	O
Stephen	O
Cook	O
,	O
who	O
cleaned	O
the	O
description	O
of	O
it	O
,	O
is	O
a	O
multiplication	B-Algorithm
algorithm	I-Algorithm
for	O
large	O
integers	O
.	O
</s>
<s>
The	O
multiplication	O
sub-operations	O
can	O
then	O
be	O
computed	O
recursively	O
using	O
Toom	B-Algorithm
–	I-Algorithm
Cook	I-Algorithm
multiplication	I-Algorithm
again	O
,	O
and	O
so	O
on	O
.	O
</s>
<s>
The	O
Karatsuba	B-Algorithm
algorithm	I-Algorithm
is	O
equivalent	O
to	O
Toom-2	O
,	O
where	O
the	O
number	O
is	O
split	O
into	O
two	O
smaller	O
ones	O
.	O
</s>
<s>
Due	O
to	O
its	O
overhead	O
,	O
Toom	O
–	O
Cook	O
is	O
slower	O
than	O
long	O
multiplication	O
with	O
small	O
numbers	O
,	O
and	O
it	O
is	O
therefore	O
typically	O
used	O
for	O
intermediate-size	O
multiplications	O
,	O
before	O
the	O
asymptotically	O
faster	O
Schönhage	B-Algorithm
–	I-Algorithm
Strassen	I-Algorithm
algorithm	I-Algorithm
(	O
with	O
complexity	O
)	O
becomes	O
practical	O
.	O
</s>
<s>
This	O
matrix	O
is	O
constructed	O
the	O
same	O
way	O
as	O
the	O
one	O
in	O
the	O
evaluation	O
step	O
,	O
except	O
that	O
it	O
's	O
d	O
×	O
d	O
.	O
We	O
could	O
solve	O
this	O
equation	O
with	O
a	O
technique	O
like	O
Gaussian	B-Algorithm
elimination	I-Algorithm
,	O
but	O
this	O
is	O
too	O
expensive	O
.	O
</s>
<s>
It	O
is	O
the	O
same	O
as	O
Karatsuba	B-Algorithm
multiplication	I-Algorithm
,	O
with	O
an	O
interpolation	O
matrix	O
of	O
:	O
</s>
