Sparse reverse Cuthill-McKee ordering

`r = symrcm(S)`

`r = symrcm(S)`

returns
the symmetric reverse Cuthill-McKee ordering of `S`

.
This is a permutation `r`

such that `S(r,r)`

tends
to have its nonzero elements closer to the diagonal. This is a good
preordering for LU or Cholesky factorization of matrices that come
from long, skinny problems. The ordering works for both symmetric
and nonsymmetric `S`

.

For a real, symmetric sparse matrix, `S`

, the
eigenvalues of `S(r,r)`

are the same as those of `S`

,
but `eig(S(r,r))`

probably takes less time to compute
than `eig(S)`

.

[1] George, Alan and Joseph Liu, *Computer
Solution of Large Sparse Positive Definite Systems*, Prentice-Hall,
1981.

[2] Gilbert, John R., Cleve Moler, and Robert
Schreiber, "Sparse Matrices in MATLAB: Design and Implementation," *SIAM
Journal on Matrix Analysis*, 1992. A slightly expanded
version is also available as a technical report from the Xerox Palo
Alto Research Center.

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