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Algorithm 836: COLAMD, a column approximate minimum degree ordering algorithm

Published: 01 September 2004 Publication History

Abstract

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 ATA and AAT, 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.

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References

[1]
Amestoy, P. R., Davis, T. A., and Duff, I. S. 1996. An approximate minimum degree ordering algorithm. SIAM J. Matrix Anal. Applic. 17, 4, 886--905.
[2]
Davis, T. A., Gilbert, J. R., Larimore, S. I., and Ng, E. G. 2004. A column approximate minimum degree ordering algorithm. ACM Trans. Math. Softw. 13, 3, xxx--xxx.
[3]
Demmel, J. W., Eisenstat, S. C., Gilbert, J. R., Li, X. S., and Liu, J. W. H. 1999. A supernodal approach to sparse partial pivoting. SIAM J. Matrix Anal. Applic. 20, 3, 720--755.
[4]
Gilbert, J. R., Moler, C., and Schreiber, R. 1992. Sparse matrices in MATLAB: Design and implementation. SIAM J. Matrix Anal. Applic. 13, 1, 333--356.
[5]
Gilbert, J. R. and Peierls, T. 1988. Sparse partial pivoting in time proportional to arithmetic operations. SIAM J. Sci. Statist. Comput. 9, 862--874.
[6]
Sigmon, K. and Davis, T. A. 2001. MATLAB Primer, Sixth Edition. Chapman & Hall / CRC Press.
[7]
The MathWorks, Inc. 2002. MATLAB External Interfaces/API, Version 6.5.

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cover image ACM Transactions on Mathematical Software
ACM Transactions on Mathematical Software  Volume 30, Issue 3
September 2004
152 pages
ISSN:0098-3500
EISSN:1557-7295
DOI:10.1145/1024074
Issue’s Table of Contents
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Publication History

Published: 01 September 2004
Published in TOMS Volume 30, Issue 3

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  1. Linear equations
  2. ordering methods
  3. sparse nonsymmetric matrices

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