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On fast factorization pivoting methods for sparse symmetric indefinite systems. (English) Zbl 1112.65022

Summary: The authors discuss 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 \(1\times 1\) and \(2\times 2\) pivots and may be supplemented by pivot perturbation techniques. We demonstrate the effectiveness and the numerical accuracy of this algorithm and also show that a high performance implementation is feasible. We also show that symmetric minimum-weighted matching strategies add an additional level of reliability to SBK. These techniques can be seen as it complement to the alternative idea of using more complete pivoting techniques during the numerical factorization. Numerical experiments validate these conclusions.

MSC:

65F05 Direct numerical methods for linear systems and matrix inversion
65F50 Computational methods for sparse matrices