Geodesic
On fast factorization pivoting methods for sparse symmetric indefinite systems
Electronic transactions on numerical analysis, Tome 23 (2006), pp. 158-179
This paper discusses new pivoting factorization methods for solving sparse symmetric indefinite systems. As opposed to many existing pivoting methods, our Supernode-Bunch-Kaufman (SBK) pivoting method dynamically selects and pivots and may be supplemented by pivot perturbation techniques. We demonstrate $\sterling $#############$\sterling $§$\ddot $###$\copyright $§ the effectiveness and the numerical accuracy of this algorithm and also show that a high performance implementation is feasible. We will also show that symmetric maximum-weighted matching strategies add an additional level of reliability to SBK. These techniques can be seen as a complement to the alternative idea of using more complete pivoting techniques during the numerical factorization. Numerical experiments validate these conclusions.
Classification : 65F05, 65F50, 05C85
Keywords: direct solver, pivoting, sparse matrices, graph algorithms, symmetric indefinite matrix, interior point optimization 
@article{ETNA_2006__23__a9,
     author = {Schenk,  Olaf and G\"artner,  Klaus},
     title = {On fast factorization pivoting methods for sparse symmetric indefinite systems},
     journal = {Electronic transactions on numerical analysis},
     pages = {158--179},
     year = {2006},
     volume = {23},
     zbl = {1112.65022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2006__23__a9/}
}
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AU  - Gärtner,  Klaus
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%0 Journal Article
%A Schenk,  Olaf
%A Gärtner,  Klaus
%T On fast factorization pivoting methods for sparse symmetric indefinite systems
%J Electronic transactions on numerical analysis
%D 2006
%P 158-179
%V 23
%U http://geodesic.mathdoc.fr/item/ETNA_2006__23__a9/
%G en
%F ETNA_2006__23__a9
Schenk,  Olaf; Gärtner,  Klaus. On fast factorization pivoting methods for sparse symmetric indefinite systems. Electronic transactions on numerical analysis, Tome 23 (2006), pp. 158-179. http://geodesic.mathdoc.fr/item/ETNA_2006__23__a9/