<s>
In	O
scientific	O
computing	O
,	O
skyline	B-Algorithm
matrix	I-Algorithm
storage	O
,	O
or	O
SKS	O
,	O
or	O
a	O
variable	B-Algorithm
band	I-Algorithm
matrix	I-Algorithm
storage	O
,	O
or	O
envelope	B-Algorithm
storage	I-Algorithm
scheme	I-Algorithm
is	O
a	O
form	O
of	O
a	O
sparse	B-Algorithm
matrix	I-Algorithm
storage	O
format	O
matrix	O
that	O
reduces	O
the	O
storage	O
requirement	O
of	O
a	O
matrix	O
more	O
than	O
banded	B-Algorithm
storage	I-Algorithm
.	O
</s>
<s>
In	O
banded	B-Algorithm
storage	I-Algorithm
,	O
all	O
entries	O
within	O
a	O
fixed	O
distance	O
from	O
the	O
diagonal	O
(	O
called	O
half-bandwidth	O
)	O
are	O
stored	O
.	O
</s>
<s>
Skyline	O
storage	O
has	O
become	O
very	O
popular	O
in	O
the	O
finite	B-Application
element	I-Application
codes	O
for	O
structural	O
mechanics	O
,	O
because	O
the	O
skyline	O
is	O
preserved	O
by	O
Cholesky	O
decomposition	O
(	O
a	O
method	O
of	O
solving	O
systems	O
of	O
linear	O
equations	O
with	O
a	O
symmetric	O
,	O
positive-definite	B-Algorithm
matrix	I-Algorithm
;	O
all	O
fill-in	O
falls	O
within	O
the	O
skyline	O
)	O
,	O
and	O
systems	O
of	O
equations	O
from	O
finite	B-Application
elements	I-Application
have	O
a	O
relatively	O
small	O
skyline	O
.	O
</s>
<s>
In	O
addition	O
,	O
the	O
effort	O
of	O
coding	O
skyline	O
Cholesky	O
is	O
about	O
same	O
as	O
for	O
Cholesky	O
for	O
banded	B-Algorithm
matrices	I-Algorithm
(	O
available	O
for	O
banded	B-Algorithm
matrices	I-Algorithm
,	O
e.g.	O
</s>
<s>
in	O
LAPACK	B-Application
;	O
for	O
a	O
prototype	O
skyline	O
code	O
,	O
see	O
)	O
.	O
</s>
<s>
The	O
same	O
heuristic	O
renumbering	O
algorithm	O
that	O
reduce	O
the	O
bandwidth	B-Algorithm
are	O
also	O
used	O
to	O
reduce	O
the	O
skyline	O
.	O
</s>
<s>
The	O
basic	O
and	O
one	O
of	O
the	O
earliest	O
algorithms	O
to	O
do	O
that	O
is	O
reverse	B-Algorithm
Cuthill	I-Algorithm
–	I-Algorithm
McKee	I-Algorithm
algorithm	I-Algorithm
.	O
</s>
<s>
However	O
,	O
skyline	O
storage	O
is	O
not	O
as	O
popular	O
for	O
very	O
large	O
systems	O
(	O
many	O
millions	O
of	O
equations	O
)	O
because	O
skyline	O
Cholesky	O
is	O
not	O
so	O
easily	O
adapted	O
for	O
massively	B-Operating_System
parallel	I-Operating_System
computing	I-Operating_System
,	O
and	O
general	O
sparse	O
methods	O
,	O
which	O
store	O
only	O
the	O
nonzero	O
entries	O
of	O
the	O
matrix	O
,	O
become	O
more	O
efficient	O
for	O
very	O
large	O
problems	O
due	O
to	O
much	O
less	O
fill-in	O
.	O
</s>
