Performance of greedy ordering heuristics for sparse Cholesky factorization

SIAM Journal on Matrix Analysis and Applications

Volumn 20, Issue 4, 1999, Pages 902-914

  Ng, Esmond G ^a   Raghavan, Padma ^b  

^a OAK RIDGE NATIONAL LABORATORY   (United States)

^b The University of Tennessee   (United States)

Author keywords

Greedy heuristics; Minimum deficiency; Minimum degree; Sparse matrix ordering

Indexed keywords

EID: 0033242226     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479897319313     Document Type: Article

References (24)

1. A. AHO, J. HOPCROFT, AND J. ULLMAN, The Design and Analysis of Computer Algorithms, Addison-Wesley, Reading, MA, 1974.
2. P. AMESTOY. T. A. DAVIS, AND I. S. DUFF, An approximate minimum degree ordering algorithm, SIAM J. Matrix Anal. Appl., 17 (1996), pp. 886-905.
3. C. ASHCRAFT, Compressed graphs and the minimum degree algorithm. SIAM J. Sci. Comput., 16 (1995), pp. 1404-1411.
4. C. ASHCRAFT AND J. W.-H. LIU, Robust Orderings of Sparse Matrices Using Multisection, Technical report ISSTECH-96-002, Boeing Computer Services, Seattle, WA, 1996.
5. P. BERMAN AND G. SCHNITGER, On the performance of the minimum degree, ordering for Gaussian elimination, SIAM J. Matrix Anal. Appl., 11 (1990), pp. 83-88.
6. E. CUTHILL, Several strategies for reducing bandwidth of matrices, in Sparse Matrices and Their Applications, D. J. Rose and R. A. Willoughby, eds., Plenum Press, New York, 1972, pp. 157-166.
7. E. CUTHILL AND J. MCKEE, Reducing the bandwidth of sparse symmetric matrices, in Proceedings 24th ACM National Conference, August 1969, ACM, New York, pp. 157-172.
8. I. DUFF, A. ERISMAN, AND J. REID, Direct Methods for Sparse Matrices, Oxford University Press, Oxford, England, 1987.
9. A. GEORGE, Computer Implementation of the Finite Element Method, Ph.D. thesis, Dept. of Computer Science, Stanford University, Stanford, CA, 1971.
10. A. GEORGE AND J. W.-H. LIU, An automatic nested dissection algorithm for irregular finite element problems, SIAM J. Numer. Anal., 15 (1978), pp. 1053-1069.
11. A. GEORGE AND J. W.-H. LIU, A quotient graph model for symmetric factorization, in Sparse Matrix Proceedings 1978, I. S. Duff and G. W. Stewart, eds., SIAM, Philadelphia, PA, 1979, pp. 154-175.
12. A. GEORGE AND J. W.-H. LIU, A fast implementation of the minimum degree algorithm using quotient graphs, ACM Trans. Math. Software, 6 (1980), pp. 337-358.
13. A. GEORGE AND J. W.-H. LIU, A minimal storage implementation of the minimum degree algorithm, SIAM J. Numer. Anal., 17 (1980), pp. 282-299.
14. A. GEORGE AND J. W.-H. LIU, Computer Solution of Large Sparse Positive Definite Systems, Prentice Hall, Englewood Cliffs, NJ, 1981.
15. A. GUPTA, Fast and Effective Algorithms for Graph Partitioning and Sparse Matrix Ordering, Technical report RC-20496, IBM Research Division, T.J. Watson Research Center, Yorktown Heights, NY, 1996.
16. B. HENDRICKSON AND E. ROTHBERG, Improving the run time and quality of nested dissection ordering, SIAM J. Sci. Comput., 20 (1999), pp. 468-489.
17. J. W.-H. LIU, Modification of the minimum degree algorithm by multiple elimination, ACM Trans. Math. Software, 11 (1985), pp. 141-153.
18. E. G.-Y. NG AND P. RAGHAVAN, Performance of Greedy Ordering Heuristics for Sparse Cholesky Factorization, manuscript, 1997.
19. S. PARTER, The use of linear graphs in Gaussian elimination, SIAM Rev., 3 (1961), pp. 119-130.
20. D. ROSE, A graph-theoretic study of the numerical solution of sparse positive definite systems of linear equations, in Graph Theory and Computing, R. C. Read, ed., Academic Press, New York, 1972, pp. 183-217.
21. E. ROTHBERG, Ordering Sparse Matrices Using Approximate Minimum Local Fill, manuscript, 1996.
22. E. ROTHBERG AND S. EISENSTAT, Node selection strategies for bottom-up sparse matrix ordering, SIAM J. Matrix Anal. Appl., 19 (1998), pp. 682-695.
23. W. TINNEY AND J. WALKER, Direct solution of sparse network equations by optimally ordered triangular factorization, Proc. IEEE, 55 (1967), pp. 1801-1809.
24. M. YANNAKAKIS, Computing the minimum fill-in is NP-complete, SIAM J. Alg. Discrete Methods, 2 (1981), pp. 77-79.