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 17 articles , 2 standard articles )

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  1. Cifuentes, Diego; Parrilo, Pablo A.: Exploiting chordal structure in polynomial ideals: a Gröbner bases approach (2016)
  2. 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)
  3. Davis, Timothy A.: Algorithm 930, FACTORIZE: an object-oriented linear system solver for MATLAB (2013)
  4. Davis, Timothy A.; Natarajan, E.Palamadai: Sparse matrix methods for circuit simulation problems (2012)
  5. Dayar, Tuǧrul: Analyzing Markov chains using Kronecker products. Theory and applications (2012)
  6. Druinsky, Alex; Toledo, Sivan: Factoring matrices with a tree-structured sparsity pattern (2011)
  7. Beuchler, Sven: Wavelet solvers for $hp$-FEM discretizations in 3D using hexahedral elements (2009)
  8. Avron, Haim; Shklarski, Gil; Toledo, Sivan: Parallel unsymmetric-pattern multifrontal sparse LU with column preordering. (2008)
  9. Bao, Yujuan; Bozkurt, ịlker N.; Dayar, Tuǧrul; Sun, Xiaobai; Trivedi, Kishor S.: Decompositional analysis of Kronecker structured Markov chains (2008)
  10. Davis, Timothy A.; Hager, William W.: A sparse proximal implementation of the LP dual active set algorithm (2008)
  11. Davis, Timothy A.; Hager, William W.: Dual multilevel optimization (2008)
  12. Buchholz, Peter; Dayar, Tugrul: Block SOR preconditioned projection methods for Kronecker structured Markovian representations (2005)
  13. Buchholz, Peter; Dayar, Tuǧrul: Block SOR for Kronecker structured representations (2004)
  14. Davis, Timothy A.: A column pre-ordering strategy for the unsymmetric-pattern multifrontal method (2004)
  15. Davis, Timothy A.; Gilbert, John R.; Larimore, Stefan I.; Ng, Esmond G.: Algorithm 836: COLAMD, a column approximate minimum degree ordering algorithm (2004)
  16. Davis, Timothy A.; Gilbert, John R.; Larimore, Stefan I.; Ng, Esmond G.: A column approximate minimum degree ordering algorithm (2004)
  17. Sethian, J. A.; Wilkening, Jon: A numerical model of stress driven grain boundary diffusion. (2004)