A numerical evaluation of HSL packages for the direct solution of large sparse, symmetric linear systems of equations

ACM Transactions on Mathematical Software

Volumn 30, Issue 3, 2004, Pages 300-325

  Gould, Nicholas I M ^a   Scott, Jennifer A ^a  

^a RUTHERFORD APPLETON LABORATORY   (United Kingdom)

Author keywords

Direct solvers; Gaussian elimination; Software; Sparse matrices; Symmetric linear systems

Indexed keywords

DIRECT SOLVERS; GAUSSIAN ELIMINATION; SPARSE MATRICES; SYMMETRIC LINEAR SYSTEMS;

COMPUTATIONAL COMPLEXITY; COMPUTER SOFTWARE; INFORMATION RETRIEVAL SYSTEMS; MATRIX ALGEBRA; PROBABILITY; PROBLEM SOLVING;

LINEAR SYSTEMS;

EID: 8344277455     PISSN: 00983500     EISSN: None     Source Type: Journal    
DOI: 10.1145/1024074.1024077     Document Type: Article

References (24)

1. AMESTOY, P., DAVIS, T., AND DUFF, I. 1996. An approximate minimum degree ordering algorithm. SIAM J. Matrix Anal. and Appl. 17, 886-905.
2. ARIOLI, M., DEMMEL, J., AND DUFF, I. 1989. Solving sparse linear systems with sparse backward error. SIAM J. Mat Anal. Appl. 10, 165-190.
3. DOLAN, E., AND MORÉ, J. 2002. Benchmarking optimization software with performance profiles. Mathe. Prog. 91, 2, 201-213.
4. DONGARRA, J., DUCROZ, J., DUFF, I., AND HAMMARLING, S. 1990. A set of Level 3 basic linear algebra subprograms. ACM Trans. Math. Softw. 16, 1, 1-17.
5. DUFF, I. 1984. Design features of a frontal code for solving sparse unsymmetric linear systems out-of-core. SIAM J. Sci. Stat. Camput. 5, 270-280.
6. DUFF, I. 2002. MA57-A new code for the solution of sparse symmetric definite and indefinite systems. Technical Report RAL-TR-2002-024, Rutherford Appleton Laboratory.
7. DUFF, I., ERISMAN, A., AND REID, J. 1986. Direct Methods for Sparse Matrices. Oxford University Press, Oxford, England.
8. DUFF, I., GOULD, N., REID, J., SCOTT, J., AND TURNER, K. 1991. Factorization of sparse symmetric indefinite matrices. IMA J. Numer. Anal. 11, 181-2044.
9. DUFF, I., GRIMES, R., AND LEWIS, J. 1989. Sparse matrix test problems. ACM Trans. Math. Softw. 15, 1-14.
10. DUFF, I. AN REID, J. 1983. The multifrontal solution of indefinite sparse symmetric linear systems. ACM Trans. Math. Softw. 9, 302-325.
11. DUFF, I. AND REID, J. 1995. MA47, a fortran code for direct solution of indefinite sparse symmetric linear systems. Report RAL-95-001, Rutherford Appleton Laboratory.
12. DUFF, I. AND REID, J. 1996. Exploiting zeros on the diagonal in the direct solution of indefinite sparse symmetric linear systems. ACM Trans. Math. Softw. 22, 2, 227-257.
13. DUFF, I. AND SCOTT, J. 1999. A frontal code for the solution of sparse positive-definite symmetric systems arising from finite-element applications. ACM Trans. Math. Softw. 25, 404-424.
14. GOULD, N. AND SCOTT, J. 2003. Complete results for a numerical evaluation of HSL packages for the direct solution of large sparse, symmetric linear systems of equations. Numerical Analysis Internal Report 2003-2, Rutherford Appleton Laboratory. Available from www.numerical.rl.ac.uk/reports/reports. shtml.
15. GOULD, N. AND TOINT, P. 2002. An iterative working-set method for large-scale non-convex quadratic programming. Appl. Numer. Math. 43, 1-2, 109-128.
16. GUPTA, A. 2002. Recent advances in direct methods or solving unsymmetric sparse systems of linear equations. ACM Trans. Math. Softw. 28, 3, 301-324.
17. HOOD, P. 1976. Frontal solution program for unsymmetric matrices. Int. J. Numer. Meth. Eng. 10, 379-400.
18. HSL. 2002. A collection of Fortran codes for large-scale scientific computation. See http://hsl.rl.ac.uk/.
19. IRONS, B. 1970. A frontal solution program for finite-element analysis. Int. J. Numer. Meth. Eng. 2, 5-32.
20. KARYPIS, G. AND KUMAR, V. 1999. A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM J. Sci. Comput. 20, 359-392.
21. LIU, J. 1992. The multifrontal method for sparse matrix solution: theory and practice. SIAM Rev. 34, 82-109.
22. REID, J. AND SCOTT, J. 1999. Ordering symmetric sparse matrices for small profile and wavefront. Inter. J. Num. Meth. Eng. 45, 1737-1755.
23. SAUNDERS, M. 1994. Sparse matrices in optimization. Presented at Sparse Days at St Girons, International meeting on Sparse Matrix Methods, St Girons, France. See http://www.stanford.edu/group/SOL/talks/saunders-stgirons.ps.
24. SCOTT, J. 1999. On ordering elements for a frontal solver. Commun. Num. Meth. Eng. 15, 309-323.