Solving unsymmetric sparse systems of linear equations with PARDISO

Future Generation Computer Systems

Volumn 20, Issue 3, 2004, Pages 475-487

  Schenk, Olaf ^a,b   G̈artner, Klaus ^c  

^a UNIVERSITY OF BASEL   (Switzerland)

^b IBM T J WATSON RESEARCH CENTER   (United States)

^c WEIERSTRASS INSTITUTE FOR APPLIED ANALYSIS AND STOCHASTICS   (Germany)

Author keywords

Computational sciences; Direct solver; Numerical linear algebra; Unsymmetric linear systems

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; COMPUTER SIMULATION; LINEAR EQUATIONS; MATRIX ALGEBRA; ROBUSTNESS (CONTROL SYSTEMS); SCHEDULING;

COMPUTATIONAL SCIENCES; DIRECT SOLVER; NUMERICAL LINEAR ALGEBRA; SPARSE SYSTEMS; UNSYMMETRIC LINEAR SYSTEMS;

PROBLEM SOLVING;

EID: 1642370513     PISSN: 0167739X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.future.2003.07.011     Document Type: Conference Paper

References (23)

1. Agarwal R.C., Gustavson F.G., Zubair M., Exploiting functional parallelism of power2 to design high-performance numerical algorithms. IBM J. Res. Dev. 38(5):1994;563-576.
2. Amestoy P.R., Duff I.S., L'Excellent J.-Y., Li X.S., Analysis and comparison of two general sparse solvers for distributed memory computers. ACM Trans. Math. Softw. 27(4):2002;338-421.
3. Amestoy P.R., Davis T.A., Duff I.S., An approximate minimum degree ordering algorithm. SIAM J. Matrix Anal. Appl. 17(4):1996;886-905.
4. Amestoy P.R., Duff I.S., L'Excellent J.-Y., Koster J., A fully asynchronous multifrontal solver using distributed dynamic scheduling. SIAM J. Matrix Anal. Appl. 23(1):2001;15-41.
5. Arioli M., Demmel J.W., Duff I.S., Solving sparse linear systems with sparse backward error. SIAM J. Matrix Anal. Appl. 10:1989;165-190.
6. Ashcraft C.C., Grimes R.G., The influence of relaxed supernode partitions on the multifrontal method. ACM Trans. Math. Softw. 15(4):1989;291-309.
7. Davis T.A., Duff I.S., An unsymmetric-pattern multifrontal method for sparse LU factorization. SIAM J. Matrix Anal. Appl. 18(1):1997;140-158.
8. T.A. Davis, UMFPACK V3.2: an unsymmetric-pattern multifrontal methods with a column pre-ordering strategy, Technical Report TR-02-2002, Computer and Information Sciences Department, University of Florida, Gainesville, FL, 2002.
9. T.A. Davis, University of Florida Sparse Matrix Collection, University of Florida, Gainesville, FL. http://www.cise.ufl.edu/~davis/sparse .
10. Demmel J., Gilbert J., Li X., An asynchronous parallel supernodal algorithm to sparse partial pivoting. SIAM J. Matrix Anal. Appl. 20(4):1999;915-952.
11. Demmel J.W., Eisenstat S.C., Gilbert J.R., Li X.S., Liu J.W.-H., A supernodal approach to sparse partial pivoting. SIAM J. Matrix Anal. Appl. 20(3):1999;720-755.
12. Duff I.S., Koster J., The design and use of algorithms for permuting large entries to the diagonal of sparse matrices. SIAM J. Matrix Anal. Appl. 20(4):1999;889-901.
13. Gupta A., Fast and effective algorithms for solving graph partitioning and sparse matrix ordering. IBM J. Res. Dev. 41(1/2):1997;171-183.
14. Gupta A., Recent advances in direct methods for solving unsymmetric sparse systems of linear equations. ACM Trans. Math. Softw. 28(3):2002;301-324.
15. A. Gupta, L. Ying, On algorithms for finding maximum matchings in bipartite graphs, Technical Report RC 21576 (97320), IBM T.J. Watson Research Center, Yorktown Heights, NY, October 25, 1999.
16. Karypis G., Kumar V., A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM J. Sci. Comput. 20(1):1998;359-392.
17. X.S. Li, J.W. Demmel, A scalable sparse direct solver using static pivoting, in: Proceedings of the Ninth SIAM Conference on Parallel Processing for Scientific Computing, San Antonio, Texas, March 22-34, 1999.
18. Liu J.W.H., Modification of the minimum-degree algorithm by multiple elimination. ACM Trans. Math. Softw. 11(2):1985;141-153.
19. Matrix Market, National Institute of Standards and Technology, Gaithersburg, MD. http://math.nist.gov/MatrixMarket.
20. Ng E.G., Peyton B.W., Block sparse Cholesky algorithms on advanced uniprocessor computers. SIAM J. Sci. Comput. 14:1993;1034-1056.
21. Schenk O., Gärtner K., Two-level scheduling in PARDISO: improved scalability on shared memory multiprocessing systems. Parall. Comput. 28:2002;187-197.
22. Schenk O., Gärtner K., Fichtner W., Efficient sparse LU factorization with left-right looking strategy on shared memory multiprocessors. BIT. 40(1):2000;158-176.
23. Sonneveld P., CGS, a fast Lanczos-type solver for nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 10:1989;36-52.