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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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On factoring a class of complex symmetric matrices without pivoting
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by Steven M. Serbin PDF
Math. Comp. 35 (1980), 1231-1234 Request permission

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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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Math. Comp. 35 (1980), 1231-1234
  • MSC: Primary 65F05
  • DOI: https://doi.org/10.1090/S0025-5718-1980-0583500-9
  • MathSciNet review: 583500