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. 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)
  2. Bu, Yiming; Carpentieri, Bruno; Shen, Zhaoli; Huang, Ting-Zhu: A hybrid recursive multilevel incomplete factorization preconditioner for solving general linear systems (2016)
  3. Jiang, Bo; Liu, Ya-Feng; Wen, Zaiwen: $L_p$-norm regularization algorithms for optimization over permutation matrices (2016)
  4. Lange, Michael; Mitchell, Lawrence; Knepley, Matthew G.; Gorman, Gerard J.: Efficient mesh management in firedrake using PETSc DMPlex (2016)
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  6. Slota, George M.; Madduri, Kamesh; Rajamanickam, Sivasankaran: Complex network partitioning using label propagation (2016)
  7. Golovach, Petr A.; Heggernes, Pinar; van ’t Hof, Pim; Manne, Fredrik; Paulusma, Daniël; Pilipczuk, Michał: Modifying a graph using vertex elimination (2015)
  8. Hager, William W.; Hungerford, James T.: Continuous quadratic programming formulations of optimization problems on graphs (2015)
  9. Janna, Carlo; Castelletto, Nicola; Ferronato, Massimiliano: The effect of graph partitioning techniques on parallel block FSAI preconditioning: a computational study (2015)
  10. Lei, Yuan: The inexact fixed matrix iteration for solving large linear inequalities in a least squares sense (2015)
  11. Li, Liang; Huang, Ting-Zhu; Jing, Yan-Fei; Ren, Zhi-Gang: Effective preconditioning through minimum degree ordering interleaved with incomplete factorization (2015)
  12. 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)
  13. Carpentieri, Bruno; Liao, Jia; Sosonkina, Masha: VBARMS: a variable block algebraic recursive multilevel solver for sparse linear systems (2014)
  14. Golovach, Petr A.; Heggernes, Pinar; Kratsch, Dieter; Saei, Reza: Subset feedback vertex sets in chordal graphs (2014)
  15. Laayouni, Lahcen; Szyld, Daniel B.: On the performance of the algebraic optimized Schwarz methods with applications (2014)
  16. Akhunov, R.R.; Kuksenko, S.P.; Salov, V.K.; Gazizov, T.R.: Sparse matrix storage formats and acceleration of iterative solution of linear algebraic systems with dense matrices (2013)
  17. Husain, S.Z.; Floryan, J.M.: Efficient solvers for the IBC method (2013)
  18. Krämer, Walter: High performance verified computing using C-XSC (2013)
  19. Mészáros, Csaba: On sparse matrix orderings in interior point methods (2013)
  20. Mizutani, Tomohiko; Yamashita, Makoto: Correlative sparsity structures and semidefinite relaxations for concave cost transportation problems with change of variables (2013)

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