## 2006.158: Factorizing complex symmetric matrices with positive definite real and imaginary parts

2006.158:
Nicholas J. Higham
(1998)
*Factorizing complex symmetric matrices with positive definite real and imaginary parts.*
Mathematics of Computation, 67 (224).
pp. 1591-1599.
ISSN 1088-6842

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DOI: 10.1090/S0025-5718-98-00978-8

## Abstract

Complex symmetric matrices whose real and imaginary parts are positive definite are shown to have a growth factor bounded by 2 for LU factorization. This result adds to the classes of matrix for which it is known to be safe not to pivot in LU factorization. Block $\mathrm{LDL^T}$ factorization with the pivoting strategy of Bunch and Kaufman is also considered, and it is shown that for such matrices only $1\times 1$ pivots are used and the same growth factor bound of 2 holds, but that interchanges that destroy band structure may be made. The latter results hold whether the pivoting strategy uses the usual absolute value or the modification employed in LINPACK and LAPACK.

Item Type: | Article |
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Uncontrolled Keywords: | Complex symmetric matrices, LU factorization, diagonal pivoting factorization, block $\mathrm{LDL^T}$ factorization, Bunch--Kaufman pivoting strategy, growth factor, band matrix, LINPACK, LAPACK |

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

MIMS number: | 2006.158 |

Deposited By: | Miss Louise Stait |

Deposited On: | 30 June 2006 |

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