Algorithm 849: A concise sparse Cholesky factorization package

ACM Transactions on Mathematical Software

Volumn 31, Issue 4, 2005, Pages 587-591

  Davis, Timothy A ^a,b  

^a UNIVERSITY OF FLORIDA   (United States)

^b University of Florida   (United States)

Author keywords

Cholesky factorization; Linear equations; Sparse matrices

Indexed keywords

ALGORITHMS; LINEAR EQUATIONS; MATRIX ALGEBRA; SET THEORY;

CHOLESKY FACTORIZATION; SPARSE MATRICES; SPARSE MATRIX ALGORITHMS; SYMMETRIC FACTORIZATION;

COMPUTER SOFTWARE;

EID: 33745213090     PISSN: 00983500     EISSN: 00983500     Source Type: Journal    
DOI: 10.1145/1114268.1114277     Document Type: Conference Paper

References (13)

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. AMESTOY, P. R., DAVIS, T. A., AND DUFF, I. S. 2004. Algorithm 837: AMD, an approximate minimum degree ordering algorithm. ACM Trans. Math. Softw. 30, 3, 381-388.
3. GEORGE, A. AND LIU, J. W. H. 1979. The design of a user interface for a sparse matrix package. ACM Trans. Math. Softw. 5, 2 (Jun.), 139-162.
4. GEORGE, A. AND LIU, J. W. H. 1981. Computer Solution of Large Sparse Positive Definite Systems. Prentice-Hall, Englewood Cliffs, NJ.
5. 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.
6. GILBERT, J. R., NG, E. G., AND PEYTON, B. W. 1994. An efficient algorithm to compute row and column counts for sparse Cholesky factorization. SIAM J. Matrix Anal. Applic. 15, 4, 1075-1091.
7. GILBERT, J. R. AND PEIERLS, T. 1988. Sparse partial pivoting in time proportional to arithmetic operations. SIAM J. Sci. Statist. Comput. 9, 862-874.
8. LIU, J. W. H. 1986. A compact row storage scheme for Cholesky factors using elimination trees. ACM Trans. Math. Softw. 12, 2 (June), 127-148.
9. LIU, J. W. H. 1990. The role of elimination trees in sparse factorization. SIAM J. Matrix Anal. Applic. 11, 1, 134-172.
10. LIU, J. W. H. 1991. A generalized envelope method for sparse factorization by rows. ACM Trans. Math. Softw. 17, 1, 112-129.
11. NG, E. G. AND PEYTON, B. W. 1993. A supernodal Cholesky factorization algorithm for shared-memory multiprocessors. SIAM J. Sci. Comput. 14, 761-769.
12. ROTHBERG, E. AND GUPTA, A. 1991. Efficient sparse matrix factorization on high-performance workstations - exploiting the memory hierarchy. ACM Trans. Math. Softw. 17, 3, 313-334.
13. STEWART, G. W. 2003. Building an old-fashioned sparse solver. Tech. rep. University of Maryland, College Park, MD. Go online to www.umd.cs.edu/~stewart.