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. De l’Isle, François; Owens, Robert G.: Superconsistent collocation methods with applications to convection-dominated convection-diffusion equations (2021)
  2. Jacquelin, Mathias; Ng, Esmond G.; Peyton, Barry W.: Fast implementation of the traveling-salesman-problem method for reordering columns within supernodes (2021)
  3. Kahl, Karsten; Lang, Bruno: Hypergraph edge elimination -- a symbolic phase for Hermitian eigensolvers based on rank-1 modifications (2021)
  4. Kashi, Aditya; Nadarajah, Sivakumaran: An asynchronous incomplete block LU preconditioner for computational fluid dynamics on unstructured grids (2021)
  5. Zdunek, Adam: Tests with FALKSOL. A massively parallel multi-level domain decomposing direct solver (2021)
  6. Zhang, Richard Y.; Lavaei, Javad: Sparse semidefinite programs with guaranteed near-linear time complexity via dualized clique tree conversion (2021)
  7. Bollhöfer, Matthias; Schenk, Olaf; Janalik, Radim; Hamm, Steve; Gullapalli, Kiran: State-of-the-art sparse direct solvers (2020)
  8. Cao, Yixin; Sandeep, R. B.: Minimum fill-in: inapproximability and almost tight lower bounds (2020)
  9. Çuğu, İlke; Manguoğlu, Murat: A parallel multithreaded sparse triangular linear system solver (2020)
  10. Saad, Yousef: Iterative methods for linear systems of equations: a brief historical journey (2020)
  11. Song, Qi; Yang, Ren; Chen, Pu: An improvement to exact reanalysis algorithm for local non-topological structural modifications (2020)
  12. Deng, Yu; Mehlitz, Patrick; Prüfert, Uwe: Optimal control in first-order Sobolev spaces with inequality constraints (2019)
  13. Evangelopoulos, Xenophon; Brockmeier, Austin J.; Mu, Tingting; Goulermas, John Y.: Continuation methods for approximate large scale object sequencing (2019)
  14. Fiore, Andrew M.; Swan, James W.: Fast Stokesian dynamics (2019)
  15. 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)
  16. 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)
  17. Bouzat, Nicolas; Bressan, Camilla; Grandgirard, Virginie; Latu, Guillaume; Mehrenberger, Michel: Targeting realistic geometry in tokamak code Gysela (2018)
  18. Eslami, Mostafa: Global range restricted GMRES for linear systems with multiple right hand sides (2018)
  19. 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)
  20. 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)

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