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Mathematics of Computation

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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
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

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