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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…
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.…
Using factorizations in Newton's method for solving general large-scale algebraic Riccati equations
Jens Saak, Steffen W. R. Werner
Continuous-time algebraic Riccati equations can be found in many disciplines in different forms. In the case of small-scale dense coefficient matrices, stabilizing solutions can be…