<s>
Every	O
submatrix	O
of	O
a	O
Cauchy	B-Algorithm
matrix	I-Algorithm
is	O
itself	O
a	O
Cauchy	B-Algorithm
matrix	I-Algorithm
.	O
</s>
<s>
The	O
determinant	O
of	O
a	O
Cauchy	B-Algorithm
matrix	I-Algorithm
is	O
clearly	O
a	O
rational	O
fraction	O
in	O
the	O
parameters	O
and	O
.	O
</s>
<s>
Hence	O
Cauchy-like	O
matrices	O
have	O
a	O
common	O
displacement	O
structure	O
,	O
which	O
can	O
be	O
exploited	O
while	O
working	O
with	O
the	O
matrix	B-Architecture
.	O
</s>
<s>
the	O
fast	B-Algorithm
multipole	I-Algorithm
method	I-Algorithm
)	O
,	O
</s>
<s>
(	O
pivoted	B-Algorithm
)	O
LU	O
factorization	O
with	O
ops	O
(	O
GKO	O
algorithm	O
)	O
,	O
and	O
thus	O
linear	O
system	O
solving	O
,	O
</s>
<s>
Here	O
denotes	O
the	O
size	O
of	O
the	O
matrix	B-Architecture
(	O
one	O
usually	O
deals	O
with	O
square	O
matrices	O
,	O
though	O
all	O
algorithms	O
can	O
be	O
easily	O
generalized	O
to	O
rectangular	O
matrices	O
)	O
.	O
</s>
