## Cholesky-like factorizations of skew-symmetric matrices

Peter Benner, Ralph Byers, Heike Fassbender, Volker Mehrmann, and David Watkins

### Abstract

Every real skew-symmetric matrix $B$ admits Cholesky-like factorizations $B = R^T J R$, where $J = \left[\begin{array}{cc} O & I \ -I & 0 \end{array}\right]$. This paper presents a backward-stable ${\cal O}(n^{3})$ process for computing such a decomposition, in which $R$ is a permuted triangular matrix. Decompositions of this type are a key ingredient of algorithms for solving eigenvalue problems with Hamiltonian structure.

Full Text (PDF) [133 KB]

### Key words

skew-symmetric matrices, matrix factorizations, Hamiltonian eigenproblems, complete pivoting.

15A23, 65F05.

### ETNA articles which cite this article

 Vol. 13 (2002), pp. 106-118 Volker Mehrmann and David Watkins: Polynomial eigenvalue problems with Hamiltonian structure Vol. 33 (2008-2009), pp. 45-52 Miloud Sadkane and Ahmed Salam: A note on symplectic block reflectors