Timothy A. Davis
John R. Gilbert
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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Software for "COLAMD, a column approximate minimum degree ordering algorithm"
- 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. Google Scholar
Digital Library
- 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. Google ScholarDigital Library
- 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. Google ScholarDigital Library
- 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. Google ScholarDigital Library
- Gilbert, J. R. and Peierls, T. 1988. Sparse partial pivoting in time proportional to arithmetic operations. SIAM J. Sci. Statist. Comput. 9, 862--874.Google ScholarDigital Library
- Sigmon, K. and Davis, T. A. 2001. MATLAB Primer, Sixth Edition. Chapman & Hall / CRC Press. Google ScholarDigital Library
- The MathWorks, Inc. 2002. MATLAB External Interfaces/API, Version 6.5.Google Scholar
Index Terms
- Algorithm 836: COLAMD, a column approximate minimum degree ordering algorithm
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