Patrick Kürschner
Katholieke Universiteit Leuven
44 Papers
179 Citations
Patrick Kürschner is an academic researcher from Katholieke Universiteit Leuven. The author has contributed to research in topics: Lyapunov function & Rank (linear algebra). The author has an hindex of 14, co-authored 44 publications. Previous affiliations of Patrick Kürschner include Max Planck Society & Leipzig University of Applied Sciences.
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Papers
An improved numerical method for balanced truncation for symmetric second-order systems
TL;DR: In this paper, the balanced truncation model order reduction for symmetric second-order systems is considered, where the large-scale generalized and structured Lyapunov equations are solved with a specially adapted low-rank alternating directions implicit (ADI) type method.
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Self-Generating and Efficient Shift Parameters in ADI Methods for Large Lyapunov and Sylvester Equations
TL;DR: Two novel shift selection strategies are proposed, based on a Galerkin projection onto the space spanned by the current ADI data, which are superior to other approaches in the majority of cases both in terms of convergence speed and required execution time.
Frequency-Limited Balanced Truncation with Low-Rank Approximations
TL;DR: It is shown in further numerical examples that frequency-limited balanced truncation generates reduced order models which are significantly more accurate in the considered frequency region.
Computing real low-rank solutions of Sylvester equations by the factored ADI method
Peter Benner,Patrick Kürschner +1 more
TL;DR: A novel low-rank expression for the associated Sylvester residual is established which enables cheap computations of the residual norm along the iteration, and which yields a reformulated factored ADI iteration which employs only an absolutely necessary amount of complex arithmetic operations and storage.
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Efficient Low-Rank Solution of Large-Scale Matrix Equations
Patrick Kürschner
- 19 Feb 2016
TL;DR: Improved low-rank ADI methods for Lyapunov and Sylvester equations are used in Newton type methods for finding approximate solutions of quadratic matrix equations in the form of symmetric, continuous-time, but also more general nonsymmetric, algebraic Riccati equations.
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