## 2006.165: Stability of the diagonal pivoting method with partial pivoting

2006.165:
Nicholas J. Higham
(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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DOI: 10.1137/S0895479895290371

## 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 |
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Uncontrolled Keywords: | symmetric indefinite matrix, diagonal pivoting method, $LDL^T$ factorization, partial pivoting, growth factor, numerical stability, rounding error analysis, LAPACK, LINPACK |

Subjects: | MSC 2000 > 15 Linear and multilinear algebra; matrix theory MSC 2000 > 65 Numerical analysis |

MIMS number: | 2006.165 |

Deposited By: | Miss Louise Stait |

Deposited On: | 03 July 2006 |

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