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Mathematics of Computation

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Factorizing complex symmetric matrices with
positive definite real and imaginary parts

Author: Nicholas J. Higham
Journal: Math. Comp. 67 (1998), 1591-1599
MSC (1991): Primary 65F05
MathSciNet review: 1474652
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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.

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Additional Information

Nicholas J. Higham
Affiliation: Department of Mathematics, University of Manchester, Manchester, M13 9PL, England

Keywords: Complex symmetric matrices, LU factorization, diagonal pivoting factorization, block $\mathrm{LDL^T}$ factorization, Bunch--Kaufman pivoting strategy, growth factor, band matrix, LINPACK, LAPACK
Received by editor(s): December 8, 1996
Article copyright: © Copyright 1998 American Mathematical Society

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