Given the square matrices A,B,D,E and the matrix C of conforming dimensions, we consider
the linear matrix equation A\mathbfXE+D\mathbfXB=C in the unknown matrix \mathbfX. Our …

The past few decades have seen a significant spurt in developing lower-order, parsimonious
models of large-scale dynamical systems used for design and control. These surrogate …

Dynamical systems are at the core of computational models for a wide range of complex
phenomena and, as a consequence, the simulation of dynamical systems has become a …

In this paper, we will discuss the problem of optimal model order reduction of bilinear control
systems with respect to the generalization of the well-known \calH_2-norm for linear …

The last two decades have seen major developments in interpolatory methods for model
reduction of large-scale linear dynamical systems. Notable advances include greater ability …

In this paper, we focus on model reduction of large-scale bilinear systems. The main
contributions are threefold. First, we introduce a new framework for interpolatory model …

In this thesis, we investigate the numerical solution of large-scale, algebraic matrix
equations. The focus lies on numerical methods based on the alternating directions implicit …

We investigate the factored alternating directions implicit (ADI) iteration for large and sparse
Sylvester equations. A novel low-rank expression for the associated Sylvester residual is …

In this article, we propose two new iterative algorithms to solve the frequency-limited
Riemannian optimization model order reduction problems of linear and bilinear systems …

In this paper, we generalize existing frameworks for H_2⊗L_2-optimal model order
reduction to a broad class of parametric linear time-invariant systems. To this end, we derive …