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. 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)
  2. 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)
  3. Hager, William W.; Hungerford, James T.; Safro, Ilya: A multilevel bilinear programming algorithm for the vertex separator problem (2018)
  4. Kovkov, D. V.; Lemtyuzhnikova, D. V.: Decomposition in multidimensional Boolean-optimization problems with sparse matrices (2018)
  5. Shioya, Akemi; Yamamoto, Yusaku: The danger of combining block red-black ordering with modified incomplete factorizations and its remedy by perturbation or relaxation (2018)
  6. Zammit-Mangion, Andrew; Rougier, Jonathan: A sparse linear algebra algorithm for fast computation of prediction variances with Gaussian Markov random fields (2018)
  7. Cerdán, J.; Marín, J.; Mas, J.: A two-level ILU preconditioner for electromagnetic applications (2017)
  8. Gould, Nicholas I. M.; Robinson, Daniel P.: A dual gradient-projection method for large-scale strictly convex quadratic problems (2017)
  9. Gupta, Anshul: Enhancing performance and robustness of ILU preconditioners by blocking and selective transposition (2017)
  10. Kamyshin, V. E.; Mazhorova, O. S.: Algorithm for solving the Navier-Stokes equations for the modeling of creeping flows (2017)
  11. Rizzuti, G.; Gisolf, A.: An iterative method for 2D inverse scattering problems by alternating reconstruction of medium properties and wavefields: theory and application to the inversion of elastic waveforms (2017)
  12. Silva, Daniele; Velazco, Marta; Oliveira, Aurelio: Influence of matrix reordering on the performance of iterative methods for solving linear systems arising from interior point methods for linear programming (2017)
  13. Tani, Mattia: A preconditioning strategy for linear systems arising from nonsymmetric schemes in isogeometric analysis (2017)
  14. Xu, Xiankun; Li, Peiwen: Distance descending ordering method: an $O(n)$ algorithm for inverting the mass matrix in simulation of macromolecules with long branches (2017)
  15. Azad, Ariful; Ballard, Grey; Buluç, Aydin; Demmel, James; Grigori, Laura; Schwartz, Oded; Toledo, Sivan; Williams, Samuel: Exploiting multiple levels of parallelism in sparse matrix-matrix multiplication (2016)
  16. Bu, Yiming; Carpentieri, Bruno; Shen, Zhaoli; Huang, Ting-Zhu: A hybrid recursive multilevel incomplete factorization preconditioner for solving general linear systems (2016)
  17. Davis, Timothy A.; Rajamanickam, Sivasankaran; Sid-Lakhdar, Wissam M.: A survey of direct methods for sparse linear systems (2016)
  18. Di Napoli, Edoardo; Polizzi, Eric; Saad, Yousef: Efficient estimation of eigenvalue counts in an interval. (2016)
  19. Fortes, M. A.; Raydan, M.; Sajo-Castelli, A. M.: Inverse-free recursive multiresolution algorithms for a data approximation problem (2016)
  20. Hasan, Mahmudul; Hossain, Shahadat; Khan, Ahamad Imtiaz; Mithila, Nasrin Hakim; Suny, Ashraful Huq: DSJM: a software toolkit for direct determination of sparse Jacobian matrices (2016)

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