COLAMD

Two codes are discussed, COLAMD and SYMAMD, that compute approximate minimum degree orderings for sparse matrices in two contexts: (1) sparse partial pivoting, which requires a sparsity preserving column pre-ordering prior to numerical factorization, and (2) sparse Cholesky factorization, which requires a symmetric permutation of both the rows and columns of the matrix being factorized. These orderings are computed by COLAMD and SYMAMD, respectively. The ordering from COLAMD is also suitable for sparse QR factorization, and the factorization of matrices of the form $A^TA$ and $AA^T$, such as those that arise in least-squares problems and interior point methods for linear programming problems. The two routines are available both in MATLAB and $C$-callable forms. They appear as built-in routines in MATLAB Version 6.0. (Source: http://dl.acm.org/)

This software is also peer reviewed by journal TOMS.


References in zbMATH (referenced in 25 articles , 2 standard articles )

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  1. 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)
  2. Koppenol, Daniël C.; Vermolen, Fred J.; Koppenol-Gonzalez, Gabriela V.; Niessen, Frank B.; van Zuijlen, Paul P. M.; Vuik, Kees: A mathematical model for the simulation of the contraction of burns (2017)
  3. Lin, Lin: Localized spectrum slicing (2017)
  4. Sencer Nuri Yeralan; Timothy A. Davis; Wissam M. Sid-Lakhdar; Sanjay Ranka: Algorithm 980: Sparse QR Factorization on the GPU (2017)
  5. Cifuentes, Diego; Parrilo, Pablo A.: Exploiting chordal structure in polynomial ideals: a Gröbner bases approach (2016)
  6. Zhang, Ye; Lin, Guang-Liang; Forssén, Patrik; Gulliksson, Mårten; Fornstedt, Torgny; Cheng, Xiao-Liang: A regularization method for the reconstruction of adsorption isotherms in liquid chromatography (2016)
  7. Ambikasaran, Sivaram: Generalized Rybicki Press algorithm. (2015)
  8. Davis, Timothy A.: Algorithm 930, FACTORIZE: an object-oriented linear system solver for MATLAB (2013)
  9. Davis, Timothy A.; Natarajan, E. Palamadai: Sparse matrix methods for circuit simulation problems (2012)
  10. Dayar, Tuǧrul: Analyzing Markov chains using Kronecker products. Theory and applications (2012)
  11. Druinsky, Alex; Toledo, Sivan: Factoring matrices with a tree-structured sparsity pattern (2011)
  12. Davis, Timothy A.; Palamadai Natarajan, Ekanathan: Algorithm 907: KLU: a direct sparse solver for circuit simulation problems (2010)
  13. Beuchler, Sven: Wavelet solvers for $hp$-FEM discretizations in 3D using hexahedral elements (2009)
  14. Avron, Haim; Shklarski, Gil; Toledo, Sivan: Parallel unsymmetric-pattern multifrontal sparse LU with column preordering. (2008)
  15. Bao, Yujuan; Bozkurt, ịlker N.; Dayar, Tuǧrul; Sun, Xiaobai; Trivedi, Kishor S.: Decompositional analysis of Kronecker structured Markov chains (2008)
  16. Davis, Timothy A.; Hager, William W.: Dual multilevel optimization (2008)
  17. Davis, Timothy A.; Hager, William W.: A sparse proximal implementation of the LP dual active set algorithm (2008)
  18. Bollhöfer, Matthias; Schenk, Olaf: Combinatorial aspects in sparse elimination methods (2006)
  19. Buchholz, Peter; Dayar, Tugrul: Block SOR preconditioned projection methods for Kronecker structured Markovian representations (2005)
  20. Hu, Yifan; Scott, Jennifer: Ordering techniques for singly bordered block diagonal forms for unsymmetric parallel sparse direct solvers. (2005)

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