### Conveners

#### Day III: Session I

- Heike Faßbender (TU Braunschweig)

#### Day III: Session II

- Bruno Iannazzo ()

We consider $\mathcal{H}_2 \otimes \mathcal{L}_2$-optimal model order reduction of parametric linear time-invariant dynamical systems, where coupled matrix integral equations arise in the first-order necessary conditions (FONC). The quality of the reduced-order model is measured using the $\mathcal{H}_2$ norm for the parametric system, which is averaged in the $\mathcal{L}_2$-norm over the...

Dynamical low-rank approximation is introduced and a numerical integrator that computes a symmetric or skew-symmetric low-rank approximation to large symmetric or skew-symmetric time-dependent matrices that are either given explicitly or are the unknown solution to a matrix differential equation is presented. We show that low-rank time-dependent matrices are reproduced exactly, and the error...

Port-Hamiltonian (pH) systems are a very important modeling structure for large classes of technical systems. In the optimal control problem for pH systems, the resulting boundary value problems and Lure/Riccati/Lyapunov have a double structure.

It is a big challenge to make use of this double structure inan effective way, but also in the solution of the associated structured eigenvalue...

Evaluating the action of a matrix function on a vector, that is $x=f(\mathcal M)v$, is an ubiquitous task in applications. When the matrix $\mathcal M$ is large, subspace projection method, such as the rational Krylov method, are usually employed.

In this work, we provide a quasi-optimal pole choice for rational Krylov methods applied to this task when $f(z)$ is either Cauchy-Stieltjes or...

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 $C_k$...

Large-scale finite-dimensional optimization problems arising from the discretization of problems involving PDEs (like in optimal control problems) sometimes admit solutions that can be well approximated by low-rank matrices. In this talk, we will exploit this low-rank approximation property by solving the optimization problem directly over the set of low-rank matrices. In particular, we...