### Speaker

Federico Poloni
(University of Pisa)

### Description

We describe a way to implement the matrix sign iteration $H_{k+1} = \frac12 (H_k^{\mathstrut}+H_k^{-1})$ on a dense Hamiltonian matrix of the form

$$H_k = \begin{bmatrix}A_k & B_kB_k^T\\ C_k^TC_k & -A_k^T & \end{bmatrix}$$ in such a way that the blocks in positions $(1,2)$ and $(2,1)$ are kept in low-rank factored form. The algorithm operates on their generators $B_k$ and $C_k$ directly, and relies on principal pivot transforms (PPTs) as its main building block; more specifically it makes use of the framework for factored-form PPTs in [Poloni, Strabic 2016]. We discuss the stability properties of the resulting algorithm, as well as applications that make use of the low-rank factors directly.

### Primary authors

Peter Benner
(Max Planck Institute for Dynamics of Complex Technical Systems)
Federico Poloni
(University of Pisa)