Related papers: An $\mathcal H_2$-Type Error Bound for Time-Limite…
Model order reduction (MOR) is often applied to spatially-discretized partial differential equations to reduce their order and hence decrease computational complexity. A reduced system can be obtained, e.g., by time-limited balanced…
When solving partial differential equations numerically, usually a high order spatial discretisation is needed. Model order reduction (MOR) techniques are often used to reduce the order of spatially-discretised systems and hence reduce…
In this paper, balancing based model order reduction (MOR) for large-scale linear discrete-time time-invariant systems in prescribed finite time intervals is studied. The first main topic is the development of error bounds regarding the…
Model order reduction (MOR) is essential in integrated circuit design, particularly when dealing with large-scale electromagnetic models extracted from complex designs. The numerous passive elements introduced in these models pose…
Model order reduction (MOR) is an important step in the design process of integrated circuits. Specifically, the electromagnetic models extracted from modern complex designs result in a large number of passive elements that introduce…
In this paper, we investigate a large-scale stochastic system with bilinear drift and linear diffusion term. Such high dimensional systems appear for example when discretizing a stochastic partial differential equations in space. We study a…
Nonlinear balanced truncation is a model order reduction technique that reduces the dimension of nonlinear systems in a manner that accounts for either open- or closed-loop observability and controllability aspects of the system. Two…
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 prescribed finite time intervals. The main emphasis is on…
This paper discusses model order reduction of LTI systems over limited frequency intervals within the framework of balanced truncation. Two new \emph{frequency-dependent balanced truncation} methods were developed, one is \emph{SF-type…
In order to solve partial differential equations numerically and accurately, a high order spatial discretization is usually needed. Model order reduction (MOR) techniques are often used to reduce the order of spatially-discretized systems…
Model reduction is a powerful tool in dealing with numerical simulation of large scale dynamic systems for studying complex physical systems. Two major types of model reduction methods for linear time-invariant dynamic systems are Krylov…
Balanced truncation is one of the most common model order reduction schemes. In this paper, we study finite-frequency model order reduction (FF-MOR) problems of linear continuous-time systems within the framework of balanced truncation…
We analyze a structure-preserving model order reduction technique for delay and stochastic delay equations based on the balanced truncation method and provide a system theoretic interpretation. Transferring error bounds based on Hankel…
We investigate model order reduction (MOR) for linear dynamical systems, where a quadratic output is defined as a quantity of interest. The system can be transformed into a linear dynamical system with many linear outputs. MOR is feasible…
Balanced truncation (BT) is a model reduction method that utilizes a coordinate transformation to retain eigen-directions that are highly observable and reachable. To address realizability and scalability of BT applied to highly stiff and…
In standard balanced truncation model order reduction, the initial condition is typically ignored in the reduction procedure and is assumed to be zero instead. However, such a reduced-order model may be a bad approximation to the full-order…
Model order reduction involves constructing a reduced-order approximation of a high-order model while retaining its essential characteristics. This reduced-order model serves as a substitute for the original one in various applications such…
The aim in model order reduction is to approximate an input-output map described by a large-scale dynamical system with a low-dimensional and cheaper-to-evaluate reduced order model. While high fidelity can be achieved by a variety of…
We analyze structure-preserving model order reduction methods for Ornstein-Uhlenbeck processes and linear S(P)DEs with multiplicative noise based on balanced truncation. For the first time, we include in this study the analysis of non-zero…
Considering the use of dynamical systems in practical applications, often only limited regions in the time or frequency domain are of interest. Therefor, it usually pays off to compute local approximations of the used dynamical systems in…