Symmetric reverse Cuthill-McKee permutation of S. Return a permutation vector p such that S
(
p,
p)
tends to have its diagonal elements closer to the diagonal than S. This is a good preordering for LU or Cholesky factorization of matrices that come from 'long, skinny' problems. It works for both symmetric and asymmetric S.The algorithm represents a heuristic approach to the NP-complete bandwidth minimization problem. The implementation is based in the descriptions found in
E. Cuthill, J. McKee: Reducing the Bandwidth of Sparse Symmetric Matrices. Proceedings of the 24th ACM National Conference, 157-172 1969, Brandon Press, New Jersey.
Alan George, Joseph W. H. Liu: Computer Solution of Large Sparse Positive Definite Systems, Prentice Hall Series in Computational Mathematics, ISBN 0-13-165274-5, 1981.