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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.