In the numerical solution of the algebraic Riccati equation A^*X+XA-XBB^*X+C^*C=0,
where A is large, sparse, and stable, and B, C have low rank, projection methods have …

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 …

In this paper, we discuss numerical methods for solving large-scale continuous-time
algebraic Riccati equations. These methods have been the focus of intensive research in …

We consider high-order splitting schemes for large-scale differential Riccati equations. Such
equations arise in many different areas and are especially important within the field of …

We apply first-and second-order splitting schemes to the differential Riccati equation. Such
equations are very important in, eg, linear quadratic regulator (LQR) problems, where they …

This paper introduces a new algorithm for solving large-scale continuous-time algebraic
Riccati equations (CARE). The advantage of the new algorithm is in its immediate and …

Quantifying the error that is induced by numerical approximation techniques is an important
task in many fields of applied mathematics. Two characteristic properties of error bounds that …

We consider operator-valued differential Lyapunov and Riccati equations, where the
operators B and C may be relatively unbounded with respect to A (in the standard notation) …

The algebraic Riccati equation (ARE) is a matrix valued quadratic equation with many
important applications in the field of control theory, such as feedback control, state …

The differential Riccati equation appears in different fields of applied mathematics like
control and system theory. Recently, Galerkin methods based on Krylov subspaces were …