Efficient numerical algorithms for the solution of large and sparse matrix Riccati and
Lyapunov equations based on the low rank alternating directions implicit (ADI) iteration have …

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 …

This paper is concerned with the numerical solution of large scale Sylvester equations AX−
XB= C, Lyapunov equations as a special case in particular included, with C having very …

Matrices with displacement structure such as Pick, Vandermonde, and Hankel matrices
appear in a diverse range of applications. In this paper, we use an extremal problem …

In this article we investigate model order reduction of large-scale systems using time-limited
balanced truncation, which restricts the well known balanced truncation framework to …

Low-rank versions of the alternating direction implicit (ADI) iteration are popular and well
established methods for the numerical solution of large-scale Sylvester and Lyapunov …

In this article we investigate model order reduction of large-scale systems using frequency-
limited balanced truncation, which restricts the well known balanced truncation framework to …

The solution of large-scale Lyapunov equations is a crucial problem for several fields of
modern applied mathematics. The low-rank Cholesky factor version of the alternating …

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 …

Matrices with displacement structure, such as Pick, Vandermonde, and Hankel matrices,
appear in a diverse range of applications. In this paper, we use an extremal problem …