7 papers
A refined nonlinear least-squares method for the rational approximation problem
Michael S. Ackermann, Linus Balicki, Serkan Gugercin +1
The adaptive Antoulas-Anderson (AAA) algorithm for rational approximation is a widely used method for the efficient construction of highly accurate rational approximations to given…
A tangential low-rank ADI method for solving indefinite Lyapunov equations
Rudi Smith, Steffen W. R. Werner
Continuous-time algebraic Lyapunov equations have become an essential tool in various applications. In the case of large-scale sparse coefficient matrices and indefinite constant t…
Second-order AAA algorithms for structured data-driven modeling
Michael S. Ackermann, Ion Victor Gosea, Serkan Gugercin +1
The data-driven modeling of dynamical systems has become an essential tool for the construction of accurate computational models from real-world data. In this process, the inherent…
Data-driven balanced truncation for second-order systems with generalized proportional damping
Sean Reiter, Steffen W. R. Werner
Structured reduced-order modeling is a central component in the computer-aided design of control systems in which cheap-to-evaluate low-dimensional models with physically meaningfu…
Deep polytopic autoencoders for low-dimensional linear parameter-varying approximations and nonlinear feedback design
Jan Heiland, Yongho Kim, Steffen W. R. Werner
Polytopic autoencoders provide low-di\-men\-sion\-al parametrizations of states in a polytope. For nonlinear PDEs, this is readily applied to low-dimensional linear parameter-varyi…
Interpolatory model reduction of dynamical systems with root mean squared error
Sean Reiter, Steffen W. R. Werner
The root mean squared error is an important measure used in a variety of applications such as structural dynamics and acoustics to model averaged deviations from standard behavior.…