ON FAST FACTORIZATION PIVOTING METHODS FOR SPARSE SYMMETRIC INDEFINITE SYSTEMS OLAF SCHENK

Abstract. This paper discusses new pivoting factorization methods for solving sparse symmetric indenite sys-tems. As opposed to many existing pivoting methods, our SupernodeBunchKaufman (SBK) pivoting method dy-namically selects and 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 implementa-tion 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