Dr. Patrick Kürschner

Computational Methods in Systems and Control Theory
Max Planck Institute for Dynamics of Complex Technical Systems

Main Focus

  • Numerical Linear Algebra
    • matrix equations and functions
    • eigenvalue problems
    • preconditioning
  • Model Order Reduction

Curriculum Vitae

Higher Education

  • 08/2010-09/2015: Ph. D. student in mathematics at the Otto-von-Guericke University of Magdeburg.
    • Obtained  degree Dr. rer. nat. in 02/2016
    • Topic of Ph.D. thesis: Efficient Low-Rank Solution of Large-Scale Matrix Equations.
    • Supervisor: Prof. Peter Benner
  • 2008-2010: student of mathematik at the Chemnitz UT. 
    • Obtained M. sc. degree in 07/2010
    • Topic of Master's thesis: Two-sided Eigenvalue Algorithms for Modal Approximation.
    • Supervisor: Prof. Peter Benner and Dr. Michiel E. Hochstenbach (TU Eindhoven).
  • 2004-2008: student of financial mathematics at the Chemnitz UT.
    • Obtained  B. sc.  degree in 03/2008:
    • Topic of Bachelor's thesis: Der Jacobi-Davidson-Algorithmus auf Parallelrechnern (in German).
    • Supervisor: Prof. Peter Benner und Dr. Matthias Pester.

Work Experience

  • 01/2011-05/2016: research associate at the Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg
  • 07/2010-12/2011: teaching assistant the faculty of mathematics,Otto-von-Guericke Universty of Magdeburg
  • 07/2010-12/2010: research associate  at the faculty of mathematics, Chemnitz UT.
  • 10/2004-07/2010: student / research assistant at the faculty of mathematics, Chemnitz UT.

Selected Publications

  1. P. Kürschner, Residual minimizing shift parameters for the low-rank ADI iteration, ArXiv e-print
    1811.05500, 2018,
    https://arxiv.org/abs/1811.05500, submitted.
  2. P. Benner, Z. Bujanovic , P. Kürschner, J. Saak, A numerical comparison of different solvers for large-scale, continuous-time algebraic Riccati equations, ArXiv e-print 1811.00850, 2018, https://arxiv.org/abs/1811.00850, submitted.
  3. Patrick Kürschner , Melina Freitag, Inexact methods for the low rank solution to large scale Lyapunov equations, ArXiv e-print 1809.06903, 2018, submitted.
  4. Patrick Kürschner, Sergey Dolgov, Kameron Decker Harris, Peter Benner: Greedy low-rank algorithm for spatial connectome regression; arXiv eprint 1808.05510, submitted, 2018.
  5. Martin Redmann, Patrick Kürschner: An Output Error Bound for Time-Limited Balanced Truncation;  System & Control Letters, 121, pp. 1 -6, 2018.
  6. Patrick Kürschner: Balanced truncation model order reduction in limited time intervals for large systems; Adv. in Comput. Math., 44(6), pp. 1821–1844, 2018.
  7. Peter Benner, Zvonimir Bujanovic, Patrick Kürschner: RADI: A low-rank ADI-type algorithm for large scale algebraic Riccati equations; Numerische Mathematik  : 138(2), pp. 301–330; 2018.
  8. Melina Freitag, Patrick Kürschner and Jennifer Pestana: GMRES Convergence Bounds for Eigenvalue Problems; Comput. Meth. Appl. Mat.,  18(2), pp. 203-222, 2018.  
  9. Peter Benner, Patrick Kürschner, Jens Saak: Frequency-Limited Balanced Truncation with Low-Rank Approximations; SIAM J. of Scientific Computing: 38(1), pp. A471–A499, 2016.
  10. Melina Freitag, Patrick Kürschner: Tuned preconditioners for inexact two-sided inverse and Rayleigh quotient iteration; Numerical Linear Algebra with Applications: 22(1), pp. 175-196;  2015.
  11. Peter Benner, Patrick Kürschner, Zoran Tomljanović, Truhar, Ninoslav: Semi-active damping optimization of vibrational systems using the parametric dominant pole algorithm; ZAMM - Journal of Applied Mathematics and Mechanics, 2015.
  12. Peter Benner, Patrick Kürschner, Jens Saak: Self-Generating and Efficient Shift Parameters in ADI Methods for Large Lyapunov and Sylvester Equations; Electronic Transaction on Numerical Analysis: 43, pp. 142-162; 2014.
  13. Peter Benner, Patrick Kürschner: Computing Real Low-rank Solutions of Sylvester equations by the Factored ADI Method; Computers and Mathematics with Applications:  67(9), pp. 1656-1672; 2014.
  14. Peter Benner, Patrick Kürschner, Jens Saak: Efficient Handling of Complex Shift Parameters in the Low-Rank Cholesky Factor ADI method; Numerical Algorithms:  62(2), pp. 225-251;  2013.
  15. Peter Benner, Patrick Kürschner, Jens Saak: An Improved Numerical Method for Balanced Truncation for Symmetric Second Order Systems; Mathematical and Computer Modelling of Dynamical Systems: 19(6), pp. 593-615; 2013.
  16. Christine Nowakowski, Patrick Kürschner, Peter Eberhard, Peter Benner: Model Reduction of an Elastic Crankshaft for Elastic Multibody Simulations; ZAMM - Journal of Applied Mathematics and Mechanics:  93(4), p. 198-216, 2013.
Full publication list available here.

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