Conveners
Plenary talk
- Peter Benner
Plenary talk
- Konrad Janik (Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg)
Plenary talk
- Fan Wang (MPI-Magdeburg)
Plenary talk
- Shaimaa Monem
Plenary talk
- Harshit Kapadia (Max Planck Institute for Dynamics of Complex Technical Systems)
Gaussian processes are a versatile tool in statistics and machine learning. They are suitable candidates to generate surrogate models that come with integrated uncertainty quantification of the reduced model. The quality of the model heavily depends on the choice of the hyperparameters and to train these on the given data many linear algebra challenges arise. In this talk we will briefly...
Finding the unique stabilizing solution $X = X^H$ of a large-scale continuous-time algebraic Riccati equation (CARE) $0 = R(X) := A^HX + XA + C^HC - XBB^HX$ with a large, sparse n-x-n matrix $A$, an $n\times m$ matrix $B$ and a $p\times n$ matrix $C$ is of interest in a number of applications. It is assumed, that $B$ and $C^H$ have full column and row rank, respectively, with $m$, $p << n$....
In this talk, we revisit the L2 optimal approximation problem through various formulations and applications, exploring its rich mathematical structure and diverse implications. We begin with the classical case where the optimal approximant is a rational function, highlighting how Hermite interpolation at specific reflected points emerges as the necessary condition for optimality. Building on...
We consider an elastic solid, e.g. a ball, which sinks towards the ground in a container filled with a liquid. The ball bounces off the bottom.
From a mathematical point of view, it is not clear what exactly happens. Assuming that the Navier-Stokes equations describe the situation, contact should not occur. The common hypothesis is that if the surface of the sphere is assumed to be...
Solving optimal control problems for transport-dominated partial differential equations (PDEs) can become computationally expensive, especially when dealing with high-dimensional systems. To overcome this challenge, we focus on developing and deriving reduced-order models that can replace the full PDE when solving the optimal control problem.
Specifically, we explore the use of the shifted...
For linear control systems, we study algebraic stability domains which are defined by polynomial inequalities in the complex plane. Based on Kharitonov's characterization via generalized Lyapunov matrix inequalities, we define a suitable pair of Gramians and a balancing transformation. Then we analyze the preservation of these stability domains by balanced truncation. For domains bounded by...
We propose a least-squares formulation for parabolic PDEs in the natural $L^2(0,T;V^*)\times H$ norm which avoids regularity assumptions on the data of the problem, which e.g. appear in the recently proposed First Order System Least Squares (FOSLS) method. For abstract parabolic equations the resulting bilinear form then is symmetric, continuous, and coercive. This among other things paves the...
