Algorithm 8xx: COLAMD, a column approximate minimum degree ordering algorithm

Journal Article · Wed Nov 01 04:00:00 EST 2000 · ACM Transactions on Mathematical Software

OSTI ID:843122

Davis, Timothy A ^[1]; Gilbert, John R; Larimore, Stefan I; Ng, Esmond G

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1. LBNL Library

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, (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'A and AA', 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.

• Research Organization: Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, CA (US)
• Sponsoring Organization: USDOE Director, Office of Science. Office of Advanced Scientific Computing Research. Mathematical, Information, and Computational Sciences Division; National Science Foundation
• DOE Contract Number: AC03-76SF00098
• OSTI ID: 843122
• Report Number(s): LBNL--47113; TR-00-006 Department of Computer and Information S
• Journal Information: ACM Transactions on Mathematical Software, Journal Name: ACM Transactions on Mathematical Software Journal Issue: 3 Vol. 30
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ALGORITHMS
FACTORIZATION
LINEAR PROGRAMMING
MATRICES
sparse unsymmetric matrices linear equations ordering methods