In the past decades, Model Order Reduction (MOR) has demonstrated its robustness and
wide applicability for simulating large-scale mathematical models in engineering and the …

Usually one avoids numerical algorithms involving operations with large, fully populated
matrices. Instead one tries to reduce all algorithms to matrix-vector multiplications involving …

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 …

Functions of matrices have been studied for as long as matrix algebra itself. Indeed, in his
seminal A Memoir on the Theory of Matrices (1858), Cayley investigated the square root of a …

The numerical treatment of partial differential equations splits into two different parts. The
first part are the discretisation methods and their analysis. This led to the author's …

We study large‐scale, continuous‐time linear time‐invariant control systems with a sparse or
structured state matrix and a relatively small number of inputs and outputs. The main …

Hierarchical matrices present an efficient way of treating dense matrices that arise in the
context of integral equations, elliptic partial differential equations, and control theory. While a …

The numerical solution of linear systems with certain tensor product structures is considered.
Such structures arise, for example, from the finite element discretization of a linear PDE on …

In this paper we construct an approximation to the solution x of a linear system of equations
A x= b of tensor product structure as it typically arises for finite element and finite difference …

Bei der Diskretisierung von Randwertaufgaben und Integralgleichungen entstehen große,
eventuell auch voll besetzte Matrizen. Es wird eine neuartige Methode dargestellt, die es …