Max-Planck-Institut für Dynamik komplexer technischer Systeme

Dr. Patrick Kürschner


Dr. Patrick Kürschner

Dr. Patrick Kürschner
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,, 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,, 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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