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. Cerdán, J.; Marín, J.; Mas, J.: A two-level ILU preconditioner for electromagnetic applications (2017)
  2. Gould, Nicholas I.M.; Robinson, Daniel P.: A dual gradient-projection method for large-scale strictly convex quadratic problems (2017)
  3. Gupta, Anshul: Enhancing performance and robustness of ILU preconditioners by blocking and selective transposition (2017)
  4. Kamyshin, V.E.; Mazhorova, O.S.: Algorithm for solving the Navier-Stokes equations for the modeling of creeping flows (2017)
  5. 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)
  6. 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)
  7. 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)
  8. Bu, Yiming; Carpentieri, Bruno; Shen, Zhaoli; Huang, Ting-Zhu: A hybrid recursive multilevel incomplete factorization preconditioner for solving general linear systems (2016)
  9. Jiang, Bo; Liu, Ya-Feng; Wen, Zaiwen: $L_p$-norm regularization algorithms for optimization over permutation matrices (2016)
  10. Lange, Michael; Mitchell, Lawrence; Knepley, Matthew G.; Gorman, Gerard J.: Efficient mesh management in firedrake using PETSc DMPlex (2016)
  11. Palitta, Davide; Simoncini, Valeria: Matrix-equation-based strategies for convection-diffusion equations (2016)
  12. Pedroche, Francisco; Rebollo, Miguel; Carrascosa, Carlos; Palomares, Alberto: On some properties of the Laplacian matrix revealed by the RCM algorithm. (2016)
  13. Rizzuti, G.; Mulder, W.A.: Multigrid-based `shifted-Laplacian’ preconditioning for the time-harmonic elastic wave equation (2016)
  14. Slota, George M.; Madduri, Kamesh; Rajamanickam, Sivasankaran: Complex network partitioning using label propagation (2016)
  15. Golovach, Petr A.; Heggernes, Pinar; van ’t Hof, Pim; Manne, Fredrik; Paulusma, Daniël; Pilipczuk, Michał: Modifying a graph using vertex elimination (2015)
  16. Hager, William W.; Hungerford, James T.: Continuous quadratic programming formulations of optimization problems on graphs (2015)
  17. Janna, Carlo; Castelletto, Nicola; Ferronato, Massimiliano: The effect of graph partitioning techniques on parallel block FSAI preconditioning: a computational study (2015)
  18. Lei, Yuan: The inexact fixed matrix iteration for solving large linear inequalities in a least squares sense (2015)
  19. Li, Liang; Huang, Ting-Zhu; Jing, Yan-Fei; Ren, Zhi-Gang: Effective preconditioning through minimum degree ordering interleaved with incomplete factorization (2015)
  20. Belmonte, Rémy; Golovach, Petr A.; Heggernes, Pinar; van’t Hof, Pim; Kamiński, Marcin; Paulusma, Daniël: Detecting fixed patterns in chordal graphs in polynomial time (2014)

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