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:

This software is also peer reviewed by journal TOMS.

References in zbMATH (referenced in 32 articles , 2 standard articles )

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  1. Fourie, Dehann; Terán Espinoza, Antonio; Kaess, Michael; Leonard, John: Characterizing marginalization and incremental operations on the Bayes tree (2021)
  2. Ploskas, Nikolaos; Sahinidis, Nikolaos V.; Samaras, Nikolaos: A triangulation and fill-reducing initialization procedure for the simplex algorithm (2021)
  3. Ke, Rihuan; Ng, Michael K.; Wei, Ting: Efficient preconditioning for time fractional diffusion inverse source problems (2020)
  4. 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)
  5. 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)
  6. Grip, N.; Pfander, G. E.: Efficient analysis of OFDM channels (2017)
  7. 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)
  8. Lin, Lin: Localized spectrum slicing (2017)
  9. Sencer Nuri Yeralan; Timothy A. Davis; Wissam M. Sid-Lakhdar; Sanjay Ranka: Algorithm 980: Sparse QR Factorization on the GPU (2017) not zbMATH
  10. Yeralan, Sencer Nuri; Davis, Timothy A.; Sid-Lakhdar, Wissam M.; Ranka, Sanjay: Algorithm 980: Sparse QR factorization on the GPU (2017)
  11. Cifuentes, Diego; Parrilo, Pablo A.: Exploiting chordal structure in polynomial ideals: a Gröbner bases approach (2016)
  12. 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)
  13. Ambikasaran, Sivaram: Generalized Rybicki Press algorithm. (2015)
  14. Davis, Timothy A.: Algorithm 930: FACTORIZE: an object-oriented linear system solver for MATLAB (2013)
  15. Davis, Timothy A.; Natarajan, E. Palamadai: Sparse matrix methods for circuit simulation problems (2012)
  16. Dayar, Tuǧrul: Analyzing Markov chains using Kronecker products. Theory and applications (2012)
  17. Druinsky, Alex; Toledo, Sivan: Factoring matrices with a tree-structured sparsity pattern (2011)
  18. Davis, Timothy A.; Palamadai Natarajan, Ekanathan: Algorithm 907: KLU: a direct sparse solver for circuit simulation problems (2010)
  19. Beuchler, Sven: Wavelet solvers for (hp)-FEM discretizations in 3D using hexahedral elements (2009)
  20. Avron, Haim; Shklarski, Gil; Toledo, Sivan: Parallel unsymmetric-pattern multifrontal sparse LU with column preordering. (2008)

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