symrcm

symrcm: Sparse reverse Cuthill-McKee ordering. 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).


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  1. Bollhöfer, Matthias; Schenk, Olaf; Janalik, Radim; Hamm, Steve; Gullapalli, Kiran: State-of-the-art sparse direct solvers (2020)
  2. Cao, Yixin; Sandeep, R. B.: Minimum fill-in: inapproximability and almost tight lower bounds (2020)
  3. Çuğu, İlke; Manguoğlu, Murat: A parallel multithreaded sparse triangular linear system solver (2020)
  4. Song, Qi; Yang, Ren; Chen, Pu: An improvement to exact reanalysis algorithm for local non-topological structural modifications (2020)
  5. Deng, Yu; Mehlitz, Patrick; Prüfert, Uwe: Optimal control in first-order Sobolev spaces with inequality constraints (2019)
  6. Evangelopoulos, Xenophon; Brockmeier, Austin J.; Mu, Tingting; Goulermas, John Y.: Continuation methods for approximate large scale object sequencing (2019)
  7. Fiore, Andrew M.; Swan, James W.: Fast Stokesian dynamics (2019)
  8. Lourenco, Christopher; Escobedo, Adolfo R.; Moreno-Centeno, Erick; Davis, Timothy A.: Exact solution of sparse linear systems via left-looking roundoff-error-free Lu factorization in time proportional to arithmetic work (2019)
  9. Rafiei, Amin; Bollhöfer, Matthias; Benkhaldoun, Fayssal: A block version of left-looking AINV preconditioner with one by one or two by two block pivots (2019)
  10. Bouzat, Nicolas; Bressan, Camilla; Grandgirard, Virginie; Latu, Guillaume; Mehrenberger, Michel: Targeting realistic geometry in tokamak code Gysela (2018)
  11. Eslami, Mostafa: Global range restricted GMRES for linear systems with multiple right hand sides (2018)
  12. Gonzaga de Oliveira, Sanderson L.; Bernardes, J. A. B.; Chagas, G. O.: An evaluation of reordering algorithms to reduce the computational cost of the incomplete Cholesky-conjugate gradient method (2018)
  13. Gonzaga de Oliveira, Sanderson L.; Bernardes, Júnior A. B.; Chagas, Guilherme O.: An evaluation of low-cost heuristics for matrix bandwidth and profile reductions (2018)
  14. Grigori, Laura; Cayrols, Sebastien; Demmel, James W.: Low rank approximation of a sparse matrix based on LU factorization with column and row tournament pivoting (2018)
  15. Hager, William W.; Hungerford, James T.; Safro, Ilya: A multilevel bilinear programming algorithm for the vertex separator problem (2018)
  16. Kovkov, D. V.; Lemtyuzhnikova, D. V.: Decomposition in multidimensional Boolean-optimization problems with sparse matrices (2018)
  17. Shioya, Akemi; Yamamoto, Yusaku: The danger of combining block red-black ordering with modified incomplete factorizations and its remedy by perturbation or relaxation (2018)
  18. Suesse, Thomas: Estimation of spatial autoregressive models with measurement error for large data sets (2018)
  19. Zammit-Mangion, Andrew; Rougier, Jonathan: A sparse linear algebra algorithm for fast computation of prediction variances with Gaussian Markov random fields (2018)
  20. Cerdán, J.; Marín, J.; Mas, J.: A two-level ILU preconditioner for electromagnetic applications (2017)

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