Stability of the diagonal pivoting method with partial pivoting

Higham, Nicholas J. (1997) Stability of the diagonal pivoting method with partial pivoting. SIAM Journal On Matrix Analysis And Applications, 18 (1). pp. 52-65. ISSN 1095-7162

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Abstract

LAPACK and LINPACK both solve symmetric indefinite linear systems using the diagonal pivoting method with the partial pivoting strategy of Bunch and Kaufman [Math. Comp., 31 (1977), pp. 163--179]. No proof of the stability of this method has appeared in the literature. It is tempting to argue that the diagonal pivoting method is stable for a given pivoting strategy if the growth factor is small. We show that this argument is false in general and give a sufficient condition for stability. This condition is not satisfied by the partial pivoting strategy because the multipliers are unbounded. Nevertheless, using a more specific approach we are able to prove the stability of partial pivoting, thereby filling a gap in the body of theory supporting LAPACK and LINPACK.

Item Type: Article
Uncontrolled Keywords: symmetric indefinite matrix, diagonal pivoting method, $LDL^T$ factorization, partial pivoting, growth factor, numerical stability, rounding error analysis, LAPACK, LINPACK
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory
MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User: Ms Lucy van Russelt
Date Deposited: 03 Jul 2006
Last Modified: 20 Oct 2017 14:12
URI: http://eprints.maths.manchester.ac.uk/id/eprint/344

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