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Dr. rer. nat. Patrick Kürschner
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Publikationen

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Eingereichte Arbeiten

@techreport{BenBKetal18a,
author = "Benner, P. and Bujanovi\'{c}, Z. and K\"{u}rschner, P. and Saak, J.",
institution = "arXiv",
note = "math.NA",
number = "1811.00850",
title = "A numerical comparison of solvers for large-scale, continuous-time algebraic {R}iccati equations",
year = 2018,
url ="https://arxiv.org/abs/1811.00850" }
A numerical comparison of solvers for large-scale, continuous-time algebraic Riccati equations;
Benner, Peter; Bujanović, Zvonimir; Kürschner, Patrick; Saak, Jens;
arXiv:1811.00850 [math.NA];
2018.
@techreport{Kue18,
author = "K\"{u}rschner, P. ",
institution = "arXiv",
note = "math.NA",
number = "1811.05500",
title = "Residual minimizing shift parameters for the low-rank ADI iteration",
year = 2018,
url ="https://arxiv.org/abs/1811.05500" }
Residual minimizing shift parameters for the low-rank ADI iteration ;
Kürschner, Patrick;;
arXiv:1811.05500 [math.NA];
2018.
@techreport{KueF18,
author = {K{\"u}rschner, P. and Freitag, M.},
title = {Inexact methods for the low rank solution to large scale Lyapunov equations}, year = 2018,
institution = {arXiv},
type = {e-print},
number = {1809.06903},
year = 2018,
note = {math.NA},
url={http://arxiv.org/abs/1809.06903} }
Inexact methods for the low rank solution to large scale Lyapunov equations;
Kürschner, Patrick; Freitag, Melina;;
arXiv:1809.06903 [math.NA];
2018.
@techreport{KueDHB18,
author = {K{\"u}rschner, P. and Dolgov, S. and Harris, K. D. and Benner P.},
title = {Greedy low-rank algorithm for spatial connectome regression},
journal = {ArXiv e-prints},
number = {1808.05510},
year = 2018,
note={Available from https://arxiv.org/abs/1808.05510. Submitted.} }
Greedy low-rank algorithm for spatial connectome regression;
Patrick Kürschner, Sergey Dolgov, Kameron Decker Harris, Peter Benner;
arXiv:1808.05510 [math.NA];
2018.
@techreport{KueK16,
author = {Kuehn, C. and K{\"u}rschner,
P.},
title = \"{Combined Error Estimates for Local Fluctuations of SPDEs}\",
journal = {ArXiv e-prints},
archivePrefix = \"arXiv\",
eprint = {1611.04629v1},
year = 2016,
month = nov,
note={Available from https://arxiv.org/abs/1611.04629v1. } }
Combined Error Estimates for Local Fluctuations of SPDEs;
Kuehn, Christian; Kürschner Patrick;
ArXiv e-prints  :  1611.04629v1;
2016.

Artikel in Zeitschriften

@article{BenBKetal18,
author = "Benner, P. and Bujanović, Z. and K{\"u}rschner, P. and Saak, J.",
title = "{RADI: A low-rank ADI-type algorithm for large scale algebraic Riccati equations}",
year = 2018,
journal = "Numer. Math.",
doi="10.1007/s00211-017-0907-5",
url="https://doi.org/10.1007/s00211-017-0907-5",
pages="301--330",
volume="138",
number="2" }
RADI: A low-rank ADI-type algorithm for large scale algebraic Riccati equations;
Benner, Peter; Bujanović, Zvonimir; Kürschner, Patrick; Saak, Jens;
Numerische Mathematik  :  vol. 138(2), pp. 301–330;
2018.
@article{FreKP18,
author = {Freitag, M. and K{\"u}rschner, P. and Pestana, J.},
title = {GMRES convergence bounds for eigenvalue problems},
journal = CMAM,
year = 2018,
pages ="203-222" doi={10.1515/cmam-2017-0017},
volume=18,
number=2 }
GMRES convergence bounds for eigenvalue problems ;
Freitag, Melina; Kürschner, Patrick; Pestana, Jennifer;
Comput. Meth. Appl. Mat.  :  18(2), pp. 203-222;
2018.
@Article{Kue18,
author="K{\"u}rschner, Patrick",
title="Balanced truncation model order reduction in limited time intervals for large systems",
journal="Advances in Computational Mathematics",
year="2018",
volume=44,
issue=6,
pages="1821--1844",
doi="10.1007/s10444-018-9608-6",
url="https://doi.org/10.1007/s10444-018-9608-6" }
Balanced truncation model order reduction in limited time intervals for large systems;
Kürschner, Patrick;
Advances in Computational Mathematics  :  44(6), pp. 1821-1844;
2018.
@article{morRedK18,
author = "Redmann, M. and Kürschner, P.",
journal = "Syst. Control Lett.",
number = "",
pages = "",
title = "{An Output Error Bound for Time-Limited Balanced Truncation}",
url = "https://doi.org/10.1016/j.sysconle.2018.08.004",
volume = "",
year = 2018 }
An Output Error Bound for Time-Limited Balanced Truncation;
Redmann, Martin; Kürschner, Patrick;
Syst. Control Lett.  :  121, pp. 1-6;
2018.
@article{BenKS16,
author = {Benner,
Peter and K{\"u}rschner, Patrick and Saak,
Jens},
title = {Frequency-Limited Balanced Truncation with Low-Rank Approximations},
journal = {SIAM Journal on Scientific Computing},
volume = {38},
number = {1},
pages = {A471-A499},
year = {2016},
doi = {10.1137/15M1030911},
URL = { http://dx.doi.org/10.1137/15M1030911},
}
Frequency-Limited Balanced Truncation with Low-Rank Approximations;
Benner, Peter; Kürschner, Patrick; Saak, Jens; ;
SIAM J. Sci. Comput.  :  38(1), pp. A471-A499;
SIAM; 2016.
@arcticle{BenKTT14,
author = {Peter Benner and Patrick K{\"u}rschner and Zoran Tomljanovi\'{c} and Ninoslav Truhar},
title = {Semi-active damping optimization of vibrational systems using the parametric dominant pole algorithm},
month = {July} year = 2016,
journal={ZAMM},
volume=96,
number=5,
pages={604--619} }
Semi-active damping optimization of vibrational systems using the parametric dominant pole algorithm;
Benner, Peter; Kürschner, Patrick; Tomljanović, Zoran; Ninoslav, Truhar;;
ZAMM  :  96(5), pp. 604-619;
WILEY-VCH; 2016.
@Article{BenKS15,
author = {Peter Benner and Patrick K{\"u}rschner and Jens Saak},
title = {Low-Rank Newton-ADI methods for Large Nonsymmetric Algebraic Riccati Equations},
year = 2015,
volume = {353},
number = {5},
pages ={1147–1167},
journal={Journal of The Franklin Institute},
doi={10.1016/j.jfranklin.2015.04.016},
}
Low-Rank Newton-ADI methods for Large Nonsymmetric Algebraic Riccati Equations;
Benner, Peter; Kürschner, Patrick; Saak, Jens;
Journal of The Franklin Institute  :  353(5), pp 1147–1167;
Elsevier; 2016.
@article {FreK14,
author = {Freitag, Melina A. and K{\"u}rschner, Patrick},
title = {Tuned preconditioners for inexact two-sided inverse and Rayleigh quotient iteration},
journal = {Numerical Linear Algebra with Applications},
issn = {1099-1506},
url = {http://onlinelibrary.wiley.com/doi/10.1002/nla.1945/},
doi = {10.1002/nla.1945},
pages = {175--196},
volume={22},
number={1},
year = {2014},
}
Tuned preconditioners for inexact two-sided inverse and Rayleigh quotient iteration;
Freitag, Melina; Kürschner, Patrick;
Numerical Linear Algebra with Applications  :  22(1), pp. 175--196;
2015.
@Article{ BenK14,
title = {Computing Real Low-rank Solutions of {S}ylvester equations by the Factored {ADI} Method},
author = {P. Benner and P. K{\"u}rschner},
journal = {Comput. Math. Appl.},
pages = {1656--1672},
volume = {67},
number = {9},
year = 2014,
issn = {0898-1221},
note = {Preprint available from \url{http://www.mpi-magdeburg.mpg.de/preprints/2013/05/}},
doi = {10.1016/j.camwa.2014.03.004} }
Computing Real Low-rank Solutions of Sylvester equations by the Factored ADI Method;
Benner, Peter; Kürschner, Patrick;
Computers and Mathematics with Applications  :  67(9), pp. 1656-1672;
Elsevier; 2014.
doi:10.1016/j.camwa.2014.03.004.
@ARTICLE{BenKS14,
author = {Peter Benner and Patrick K{\"u}rschner and Jens Saak},
title = {Self-Generating and Efficient Shift Parameters in ADI Methods for Large Lyapunov and Sylvester Equations},
year = 2014,
journal = {Electronic Transaction on Numerical Analysis},
number=43,
pages={142-162},
doi={10.17617/2.2071065},
note = {Early version available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}
Self-Generating and Efficient Shift Parameters in ADI Methods for Large Lyapunov and Sylvester Equations;
Benner, Peter; Kürschner, Patrick; Saak, Jens;
Electronic Transaction on Numerical Analysis   :  43, pp. 142-162;
2014.
@article {BenKS12,
author = {Benner, Peter and K{\"u}rschner, Patrick and Saak, Jens},
affiliation = {Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstraße 1, 39106 Magdeburg, Germany},
title = {Efficient handling of complex shift parameters in the low-rank Cholesky factor ADI method},
journal = {Numerical Algorithms},
publisher = {Springer U.S.},
issn = {1017-1398},
keyword = {Computer Science},
volume={62},
issue={2},
pages = {225-251},
url = {http://dx.doi.org/10.1007/s11075-012-9569-7},
note = {10.1007/s11075-012-9569-7},
}
Efficient Handling of Complex Shift Parameters in the Low-Rank Cholesky Factor ADI method;
Benner, Peter; Kürschner, Patrick; Saak, Jens;
Numerical Algorithms  :  Volume 62, Issue 2, pages 225-251, February 2013 ;
Springer U.S.; 2013.
DOI: 10.1007/s11075-012-9569-7
also available as preprint MPIMD/11-08.
@ARTICLE{morNowEtal12,
author = {Nowakowski, C. and K{\"u}rschner, P. and Eberhard,
P. and Benner, P.},
title = {Model reduction of an elastic crankshaft for elastic multibody simulations},
journal = {ZAngewMathMech},
publisher = {WILEY-VCH Verlag},
volume={93},
number={4},
pages={198--216},
issn = {1521-4001},
url = {http://dx.doi.org/10.1002/zamm.201200054},
doi = {10.1002/zamm.201200054},
keywords = {Elastic multibody systems,
odel order reduction,
rylov, SVD, ADI.},
year = 2012,
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}
Model Reduction of an Elastic Crankshaft for Elastic Multibody Simulations;
Nowakowski, Christine; Kürschner, Patrick; Eberhard, Peter; Benner, Peter ;
ZAMM - Journal of Applied Mathematics and Mechanics  :  Vol. 93(4), pp. 198 - 216;
WILEY-VCH Verlag; 2013.
accepted; also available as preprint MPIMD/12-07.
@Article{BenKS13,
author = {Peter Benner and Patrick Kürschner and Jens Saak},
title = {An Improved Numerical Method for Balanced Truncation for Symmetric Second Order Systems},
year = 2013,
journal = {Mathematical and Computer Modelling of Dynamical Systems},
volume=19,
number=6,
pages={593--615},
doi = {10.1080/13873954.2013.794363},
note = {Early Version available from \url{http://www.mpi-magdeburg.mpg.de/preprints/2012/20/}},
}
An Improved Numerical Method for Balanced Truncation for Symmetric Second Order Systems;
Peter Benner, Patrick Kürschner, Jens Saak;
Mathematical and Computer Modelling of Dynamical Systems  :  Vol. 19(6), pages 593-615;
2013.
DOI:10.1080/13873954.2013.794363 Also available as Preprint MPIMD/12-20.

Beiträge zu Tagungsbänden

@inproceedings{FreK13,
Title = {Inner-outer methods for large-scale two-sided eigenvalue problems},
Author = {Melina Freitag and Patrick K{\"u}rschner},
Booktitle = {Oberwolfach Report - Numerical Solution of PDE Eigenvalue Problems},
Pages = {86--89},
Year = {2013},
Volume = {56},
doi = {10.4171/OWR/2013/56} }
Inner-outer methods for large-scale two-sided eigenvalue problems;
Freitag, Melina; Kürschner, Patrick;
Numerical Solution of PDE Eigenvalue Problems  :  Oberwolfach Report 56/2013;
2013.
doi:10.4171/OWR/2013/56.
@article {BenKS13,
author = {Benner, Peter and Kürschner, Patrick and Saak, Jens},
title = {A Reformulated Low-Rank {ADI} Iteration with Explicit Residual Factors},
journal = {PAMM},
volume = {13},
number = {1},
publisher = {WILEY-VCH Verlag},
issn = {1617-7061},
url = {http://dx.doi.org/10.1002/pamm.201310273},
doi = {10.1002/pamm.201310273},
pages = {585--586},
year = {2013},
}
A Reformulated Low-Rank ADI Iteration with Explicit Residual Factors;
Peter Benner, Patrick Kürschner and Jens Saak;
Proceedings in Applied Mathematics and Mechanics  :  Volume 13, Issue 1, December 2013, Pages: 585–586;
Wiley-VCH Verlag; 2013.
DOI: 10.1002/pamm.201310273.
@article{morBenKS12,
title = "Improved second-order balanced truncation for symmetric systems",
journal = "IFAC Proceedings Volumes",
volume = "45",
number = "2",
pages = "758 - 762",
year = "2012",
editor = "Troch,
I. and Breitenecker,
F.",
note = "7th Vienna International Conference on Mathematical Modelling",
issn = "1474-6670",
doi = "10.3182/20120215-3-AT-3016.00134",
author = "Jens Saak and Peter Benner and Patrick K{\"u}rschner",
}
Improved second-order balanced truncation for symmetric systems;
Benner, Peter; Kürschner, Patrick; Saak, Jens;
IFAC Proceedings Volumes   :  45(2):758 - 762;
2012.
Proceedings of 7th Vienna International Conference on Mathematical Modelling.
@article{morBenKS12,
title = "A Goal-Oriented Dual LRCF-ADI for Balanced Truncation",
journal = "IFAC Proceedings Volumes",
volume = "45",
number = "2",
pages = "752 - 757",
year = "2012",
editor = "Troch, I. and Breitenecker, F.",
note = "7th Vienna International Conference on Mathematical Modelling", issn = "1474-6670",
doi = "10.3182/20120215-3-AT-3016.00133", author = "Jens Saak and Peter Benner and Patrick K{\"u}rschner", }
A Goal-Oriented Dual LRCF-ADI for Balanced Truncation.;
Peter Benner, Patrick Kürschner, Jens Saak;
IFAC Proceedings Volumes  :  45(2):752 - 757;
2012.
Proceedings of 7th Vienna International Conference on Mathematical Modelling.
@InProceedings{BenKS12b,
author = {P. Benner and P. K\"u rschner and J. Saak},
title = {Avoiding complex arithmetic in the low-rank ADI method efficiently},
journal = PAMM,
volume = {12},
number = {1},
pages = {639-640},
publisher = {WILEY-VCH Verlag},
issn = {1617-7061},
year = {2012},
note = {DOI: 10.1002/pamm.201210308},
}
Avoiding complex arithmetic in the low-rank ADI method efficiently;
Peter Benner; Patrick Kürschner; Jens Saak;
Proceedings in Applied Mathematics and Mechanics  :  
Wiley InterScience; 2012.
Pages: 639–640, DOI: 10.1002/pamm.201210308.
CA3Optimale FE-Reduktion, Moderne Modellreduktion elastischer Bauteile für die Simulation flexibler Mehrkörpersysteme
Benner, Peter; Eberhard, Peter; Knoll, Gunter; Kürschner, Patrick; Nowakowski, Christine; Ochse, Gerald;
FVV Frühjahrstagung 2011, Frankfurt a.M.: Forschungsvereinigung Verbrennungskraftmaschinen e.V.  :  Heft R553, pp. 175-197;
2011.
@INPROCEEDINGS{BenHK11,
author={Benner, P. and Hochstenbach, M.E. and K\"u rschner, P.},
booktitle={Communications, Computing and Control Applications (CCCA), 2011 International Conference on},
title={Model order reduction of large-scale dynamical systems with {J}acobi-{D}avidson style eigensolvers},
year={2011},
month={march},
volume={},
number={},
pages={1 -6},
doi={10.1109/CCCA.2011.6031208},
url={http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6031208} }
Model order reduction of large-scale dynamical systems with Jacobi-Davidson style eigensolvers;
Benner, Peter; Hochstenbach, Michiel; Kürschner, Patrick;
International Conference on Communications, Computing and Control Applications, 2011 (CCCA11)  :  
IEEE; 2011.
IEEE Catalog Number: CFP1154M-ART
DOI: 10.1109/CCCA.2011.6031208 .
@article{BenHK11,
author = {Benner,
P. and K\"urschner, P. and Hochstenbach, M.},
title = {{T}wo-sided harmonic subspace extractions for the generalized eigenvalue problem},
journal = {PAMM},
volume = {11},
number = {1},
publisher = {WILEY-VCH Verlag},
issn = {1617-7061},
url = {http://dx.doi.org/10.1002/pamm.201110359},
doi = {10.1002/pamm.201110359},
pages = {739--740},
year = {2011},
}
Two-sided harmonic subspace extractions for the generalized eigenvalue problem;
Benner, Peter; Hochstenbach, Michiel; Kürschner, Patrick;
Proceedings in Applied Mathematics and Mechanics  :  Volume 11, Issue 1, pages 741–742, December 2011;
Wiley InterScience; 2011.
doi: 10.1002/pamm.201110359.

Arbeitsberichte

@TECHREPORT{BenKS12c,
author = {P. Benner and P. K\"u rschner and J. Saak},
title = {Real versions of low-rank ADI methods with complex shifts},
number = {MPIMD/12-11},
year = 2012,
type = {Max Planck Institute Magdeburg Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}
Real versions of low-rank ADI methods with complex shifts;
Peter Benner; Patrick Kürschner; Jens Saak;
MPI Magdeburg Preprints MPIMD/12-11;
2012.

Qualifizierungsarbeiten

@PhdThesis{Kue16,
author = {Patrick K{\"u}rschner},
title = Efficient Low-Rank Solution of Large-Scale Matrix Equations},
school = {OvGU Magdeburg},
year = 20016,
month = {April},
publisher={Shaker Verlag} }
Efficient Low-Rank Solution of Large-Scale Matrix Equations;
P. Kürschner;
Shaker Verlag; 2016.
@MASTERSTHESIS{Kuer10,
author = {P. K\"urschner},
title = {Two-Sided Eigenvalue Methods for Modal Approximation},
school = {Chemnitz University of Technology,
Department of Mathematics,
Germany},
year = {2010},
owner = {kupa},
timestamp = {2010.07.16} }
Two-Sided Eigenvalue Methods for Modal Approximation;
Patrick Kürschner;
Chemnitz University of Technology; 2010.
T1Der Jacobi-Davidson Algorithmus auf Parallelrechnern
Patrick Kürschner;
Chemnitz University of Technology; 2008.
Bachelor thesis, in german.