Abstract
The problem of finding good numerical preprocessing methods for the solution of symmetric indefinite systems is considered. Special emphasis is put on symmetric maximum-weighted matching strategies. The aim is to permute large elements of the matrix to diagonal blocks. Several variants for the block sizes are examined and the accuracies of the solutions are compared. It is shown that maximum-weighted matchings improve the accuracy of sparse direct linear solvers. The use of a strategy called full cycles results in an accurate and reliable factorization. Numerical experiments validate these conclusions.
This work was supported by the Swiss Commission of Technology and Innovation under contract number 7036.1 ENS-ES, and the Strategic Excellence Positions on Computational Science and Engineering of the Swiss Federal Institute of Technology, Zurich.
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References
Benzi, M., Haws, J.C., Tuma, M.: Preconditioning highly indefinite and nonsymmetric matrices. SIAM J. Scientific Computing 22(4), 1333–1353 (2000)
Dolan, E.D., Moré, J.J.: Benchmarking optimization software with performance profiles. Mathematical Programming 91(2), 201–213 (2002)
Duff, I.S.: MA57 – a code for the solution of sparse symmetric definite and indefinite systems. ACM Transactions on Mathematical Software 30(2), 118–144 (2004)
Duff, I.S., Gilbert, J.R.: Maximum-weighted matching and block pivoting for symmetric indefinite systems. In: Abstract book of Householder Symposium XV, June 17-21 (2002)
Duff, I.S., Koster, J.: On algorithms for permuting large entries to the diagonal of a sparse matrix. SIAM J. Matrix Analysis and Applications 22(4), 973–996 (2001)
Duff, I.S., Pralet, S.: Strategies for scaling and pivoting for sparse symmetric indefinite problems. Technical Report TR/PA/04/59, CERFACS, Toulouse, France (2004)
Gould, N.I.M., Scott, J.A.: A numerical evaluation of HSL packages for the direct solution of large sparse, symmetric linear systems of equations. ACM Transactions on Mathematical Software 30(3), 300–325 (2004)
Gupta, A., Ying, L.: 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)
Karypis, G., Kumar, V.: A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM J. Scientific Computing 20(1), 359–392 (1998)
Schenk, O., Gärtner, K.: On fast factorization pivoting methods for sparse symmetric indefinite systems. Technical Report CS-2004-004, Department of Computer Science, University of Basel (2004) (submitted)
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Röllin, S., Schenk, O. (2006). Maximum-Weighted Matching Strategies and the Application to Symmetric Indefinite Systems. In: Dongarra, J., Madsen, K., Waśniewski, J. (eds) Applied Parallel Computing. State of the Art in Scientific Computing. PARA 2004. Lecture Notes in Computer Science, vol 3732. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11558958_97
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DOI: https://doi.org/10.1007/11558958_97
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