<s>
Cyclic	B-Algorithm
reduction	I-Algorithm
is	O
a	O
numerical	B-Algorithm
method	I-Algorithm
for	O
solving	O
large	O
linear	O
systems	O
by	O
repeatedly	O
splitting	O
the	O
problem	O
.	O
</s>
<s>
The	O
method	O
only	O
applies	O
to	O
matrices	O
that	O
can	O
be	O
represented	O
as	O
a	O
(	O
block	O
)	O
Toeplitz	B-Algorithm
matrix	I-Algorithm
,	O
such	O
problems	O
often	O
arise	O
in	O
implicit	O
solutions	O
for	O
partial	O
differential	O
equations	O
on	O
a	O
lattice	O
.	O
</s>
<s>
Transforming	O
from	O
the	O
spatial	O
domain	O
and	O
restating	O
the	O
PDE	O
is	O
called	O
a	O
spectral	B-Algorithm
method	I-Algorithm
,	O
Fourier	O
analysis	O
and	O
cyclic	B-Algorithm
reduction	I-Algorithm
are	O
combined	O
in	O
the	O
FACR	O
algorithm	O
which	O
is	O
explained	O
in	O
Numerical	O
Recipes	O
–	O
see	O
19.4	O
Fourier	O
and	O
Cyclic	B-Algorithm
Reduction	I-Algorithm
Methods	O
for	O
Boundary	O
Value	O
Problems	O
.	O
</s>
