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On factoring a class of complex symmetric matrices without pivoting


Author: Steven M. Serbin
Journal: Math. Comp. 35 (1980), 1231-1234
MSC: Primary 65F05
DOI: https://doi.org/10.1090/S0025-5718-1980-0583500-9
MathSciNet review: 583500
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Abstract: Let $\mathcal {A} = \mathcal {B} + i\mathcal {C}$ be a complex, symmetric $n \times n$ matrix with $\mathcal {B}$ and $\mathcal {C}$ each real, symmetric and positive definite. We show that the LINPACK diagonal pivoting decomposition ${\mathcal {U}^{ - 1}}\mathcal {A}{({\mathcal {U}^{ - 1}})^T} = \mathcal {D}$ proceeds without the necessity for pivoting. In particular, when $\mathcal {B}$ and $\mathcal {C}$ are band matrices, bandwidth is preserved.


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Article copyright: © Copyright 1980 American Mathematical Society