On factoring a class of complex symmetric matrices without pivoting

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.