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Forschungsaktivität ohne Förderung

Große schwach besetzte Matrixgleichungen




Projektleiter:
  • Prof. Dr. Peter Benner
    Max-Planck-Institut für Dynamik komplexer technischer Systeme Magdeburg,
    Computational Methods in Systems and Control Theory,
    Sandtorstr. 1, 39106 Magdeburg
    Tel: +49 (0)391-6110-450
    E-mail: benner@mpi-magdeburg.mpg.de
Mitarbeiter:
  • Martin Köhler
    Max-Planck-Institut für Dynamik komplexer technischer Systeme Magdeburg,
    Computational Methods in Systems and Control Theory,
    Sandtorstr. 1, 39106 Magdeburg
    Tel: +49 (0)391-6110-445
    E-mail: koehlerm@mpi-magdeburg.mpg.de
  • Patrick Kürschner
    Max-Planck-Institut für Dynamik komplexer technischer Systeme Magdeburg,
    Computational Methods in Systems and Control Theory,
    Sandtorstr. 1, 39106 Magdeburg
    Tel: +49 (0)391-6110-424
    E-mail: kuerschner@mpi-magdeburg.mpg.de
  • Dr. Jens Saak
    Max-Planck-Institut für Dynamik komplexer technischer Systeme Magdeburg,
    Computational Methods in Systems and Control Theory,
    Sandtorstr. 1, 39106 Magdeburg
    Tel: +49 (0)391-6110-216
    E-mail: saak@mpi-magdeburg.mpg.de
  • Dr. Hermann Mena
    Department of Mathematics
    Escuela Politécnica Nacional
    Ladrón de Guevara E11-253
    Casilla postal: 17-01-2759
    Quito-Ecuador
    Tel: +593-2-2507-144
    E-mail: hermann.mena@epn.edu.ec
Laufzeit: seit 2000

Projektbeschreibung:
Wir untersuchen numerische Lösungsverfahren für große schwach besetzte lineare und quadratische Matrixgleichungen. Ein besonderer Fokus liegt dabei auf großen zeitkontinuierlichen Sylvester, Lyapunov und Riccatigleichungen wie sie in Modellreduktion und linear quadratischen regelungs problemen mit partiellen Differentialgleichungen auftreten. Die verwendeten Methoden beruhen weitestgehend auf der Niedrig-Rang-ADI Iteration und neue Erkenntnisse fliessen direkt in die Entwicklung unserer Softwarebibliothek und MATLAB Toolbox M.E.S.S. ein.


Veröffentlichungen:

@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{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.
@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{morLanSS16,
author = {N. Lang and J. Saak and T. Stykel},
title = {Balanced truncation model reduction for linear time-varying systems},
journal = MCMDS,
volume = 22,
number = 4,
pages = {267--281},
year = 2016,
doi = {10.1080/13873954.2016.1198386},
URL = {http://dx.doi.org/10.1080/13873954.2016.1198386} }
Balanced truncation model reduction for linear time-varying systems;
Norman Lang, Jens Saak, Tatjana Stykel;
Mathematical and Computer Modelling of Dynamical Systems  :  Volume 22, Issue 4, Pages 267-281;
Taylor & Francis; 2016. ISBN/ISSN: 1387-3954, 1744-505
DOI: 10.1080/13873954.2016.1198386, also available as preprint from https://www.tu-chemnitz.de/mathematik/csc/2015/.
@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. ISBN/ISSN: 978-3-8440-4385-3
@ARTICLE{LanMS15,
author = {Lang,
N. and Mena,
H. and Saak,
J.},
title = {On the benefits of the $LDL^T$ factorization for large-scale differential matrix equation solvers },
journal = {Linear Algebra and its Applications},
publisher = {Elsevier},
volume = {480},
month = sep,
year = 2015,
pages = {44--71},
doi = {10.1016/j.laa.2015.04.006},
}
On the benefits of the LDLT factorization for large-scale differential matrix equation solvers;
Norman Lang, Hermann Mena, Jens Saak;
Linear Algebra and its Applications  :  Volume 480, Pages. 44-71;
Elsevier; 2015.
DOI: 10.1016/j.laa.2015.04.006.
@article{LanSS15,
title = {Towards Practical Implementations of Balanced Truncation for {LTV} Systems},
journal = {IFAC-PapersOnLine},
volume = {48},
number = {1},
pages = {7--8},
year = {2015},
issn = {2405-8963},
doi = {http://dx.doi.org/10.1016/j.ifacol.2015.05.135},
url = {http://www.sciencedirect.com/science/article/pii/S2405896315001366},
author = {N.~Lang and J.~Saak and T.~Stykel},
}
Towards Practical Implementations of Balanced Truncation for LTV Systems;
Norman Lang, Jens Saak, Tatjana Stykel;
IFAC-PapersOnLine  :  Volume 48, Issue 1, Pages: 7-8;
Elsevier; 2015. ISBN/ISSN: 2405-8963
DOI: 10.1016/j.ifacol.2015.05.135.
@String{PAMM = \"Proc. Appl. Math. Mech.\" }
@String{WileyVCH = \"WILEY-VCH Verlag\" }
@Article{BarKPetal14,
author = {B. Baran and M. Köhler and N. Prasad and J. Saak},
title = {Numerical Solution of Large Scale Sparse Matrix Equations in {P}ython},
journal = PAMM,
year = {2014},
volume = 14,
number = 1,
pages = {959--960},
month = dec }
Numerical Solution of Large Scale Sparse Matrix Equations in Python;
B. Baran, M. Köhler, N. Prasad and J. Saak;
Proc. Appl. Math. Mech.  :  Volume 14, Issue 1, Pages: 959-960;
WILEY-VCH Verlag; 2014.
DOI: 10.1002/pamm.201410460.
346A factored variant of the Newton iteration for the solution of algebraic Riccati equations via the matrix sign function;
Benner, Peter; Ezzatti, Pablo;Quintana-Ortí, Enrique S. ; Remón, Alfredo; ;
Numerical Algorithms  :  Vol. 62 Issue 2;
Springer US; 2014. ISBN/ISSN: 1017-1398
@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. ISBN/ISSN: 0898-1221
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.
@String{PAMM = \"Proc. Appl. Math. Mech.\" }
@String{WileyVCH = \"WILEY-VCH Verlag\" }
@Article{LanMS14,
title = {An {$LDL^T$} factorization based {ADI} algorithm for solving large scale differential matrix equations},
author = {N. Lang and H. Mena and J. Saak},
publisher = WileyVCH,
journal = PAMM,
volume = 14,
number = 1,
year = 2014,
url = {http://onlinelibrary.wiley.com/doi/10.1002/pamm.201410394/abstract},
doi = {10.1002/pamm.201410394},
pages = {827--828} }
An LDLT factorization based ADI algorithm for solving large-scale differential matrix equations;
Norman Lang, Hermann Mena, Jens Saak;
Proceedings in Applied Mathematics and Mechanics  :  Volume 14, Issue 1, Pages: 827–828;
WILEY-VCH Verlag; 2014.
DOI: 10.1002/pamm.201410394.
@Article{BenS13,
author = {P. Benner and J. Saak},
title = {Numerical solution of large and sparse continuous time algebraic matrix Riccati and Lyapunov equations: a state of the art survey },
journal = {GAMM Mitteilungen},
year = 2013,
volume = 36,
number = 1,
pages = {32--52},
month = {August},
DOI = {10.1002/gamm.201310003} }
Numerical Solution of Large and Sparse Continuous Time Algebraic Matrix Riccati and Lyapunov Equations: A State of the Art Survey;
Benner, Peter and Saak, Jens;
GAMM-Reports  :  vol 6 No 1 pages 32-52;
2013. ISBN/ISSN: 1522-2608
Preprint available at http://www.mpi-magdeburg.mpg.de/preprints/2013/07/ DOI:10.1002/gamm.201310003.
@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. ISBN/ISSN: 1017-1398
DOI: 10.1007/s11075-012-9569-7
also available as preprint MPIMD/11-08.
@TECHREPORT{MPIMD13-22,
author = { Björn Baran and Martin Köhler and Nitin Prasad and Jens Saak},
title = {Interfacing C-M.E.S.S. with Python},
number = {MPIMD/13-22},
month = nov,
year = 2013,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}
Interfacing C-M.E.S.S. with Python;
Björn Baran, Martin Köhler, Nitin Prasad, Jens Saak;
MPIMD/13-22;
MPI Magdeburg Preprints; 2013.
@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{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.
@INPROCEEDINGS{SaaUV13,
author = {Jens Saak and M. Monir Uddin and Matthias Voigt},
title = {Modellreduktion für strukturierte {I}ndex-3-{S}ysteme},
booktitle= {Tagungsband des GMA-Fachausschusses 1.30 \glqq Modellbildung,
Identifikation und Simulation in der Automatisierungstechnik\grqq},
pages = {180--190},
editor = {Oliver Sawodny and J\"urgen Adamy},
month = {November},
year = {2013},
publisher = {Technische Universit\"at Darmstadt,
Institut f\"ur Automatisierungstechnik und Mechatronik},
isbn = {978-3-9815012-5-4},
}
Modellreduktion für strukturierte Index-3-Systeme
Saak, Jens; Uddin, M. Monir; Voigt, Matthias;
in Sawodny, Oliver; Adamy, Jürgen: Tagungsband des GMA-Fachausschusses 1.30 „Modellbildung, Identifikation und Simulation in der Automatisierungstechnik“  :  pp. 180 - 190;
Technische Universität Darmstadt, Institut für Automatisierungstechnik und Mechatronik; 2013. ISBN/ISSN: 978-3-9815012-5-4
@InProceedings{MacS12,
author = {T. Mach and J. Saak},
title = {How Competitive is the ADI for Tensor Structured Equations?},
journal = {PAMM},
volume = {12},
number = {1},
publisher = {WILEY-VCH Verlag},
issn = {1617-7061},
year = {2011},
note = {DOI: 10.1002/pamm.201210306},
}
How Competitive is the ADI for Tensor Structured Equations?;
Mach, Thomas; Saak, Jens;
Proceedings in Applied Mathematics and Mechanics  :  
Wiley InterScience; 2012.
Pages: 635–636, DOI: 10.1002/pamm.201210306.
@INPROCEEDINGS{morBenKS12,
author = {Peter Benner,
Patrick K{\"u}rschner,
Jens Saak },
title = {A Goal-Oriented Dual LRCF-ADI for Balanced Truncation},
booktitle = {7th Vienna International Conference on Mathematical Modelling},
year = 2012,
organization = {Vienna Univ. of Technology},
editor = {I. Troch and F. Breitenecker},
series = {IFAC-PapersOnlines,
Mathematical Modelling},
volume={7},
number = {1},
pages={752-757} }
A Goal-Oriented Dual LRCF-ADI for Balanced Truncation.;
Peter Benner, Patrick Kürschner, Jens Saak;
in I. Troch and F. Breitenecker: 7th Vienna International Conference on Mathematical Modelling  :  IFAC-PapersOnline, Mathematical Modelling;
2012. ISBN/ISSN: 978-3-902823-23-6
@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.
@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.
@TECHREPORT{MPIMD11-11,
author = { Peter Benner,
Martin Köhler,
Jens Saak},
title = {{Sparse-Dense Sylvester Equations in H2-Model Order Reduction},
institution = {Max Planck Institute Magdeburg Preprints},
year = 2011,
number = {MPIMD/11-11},
month = {December} }
Sparse-Dense Sylvester Equations in H₂-Model Order Reduction;
Benner, Peter; Köhler, Martin; Saak, Jens;
2011.
@TECHREPORT{MPIMD11-12,
author = {Thomas Mach,
Jens Saak},
title = {Towards an ADI iteration for Tensor Structured Equations},
institution = {Max Planck Institute Magdeburg Preprints},
year = 2011,
number = {MPIMD/11-12},
month = {December} }
Towards an ADI iteration for Tensor Structured Equations;
Mach, Thomas; Saak, Jens;
Max Planck Institute Magdeburg Preprints, MPIMD/11-12;
2011.
16 pages.
@TechReport{BenS10,
author = {P. Benner and J. Saak},
title = {{A Galerkin-Newton-ADI Method for Solving Large-Scale Algebraic Riccati Equations}},
institution = {SPP1253},
note = {\url{http://www.am.uni-erlangen.de/home/spp1253/wiki/index.php/Preprints}},
year = 2010,
number = {SPP1253-090},
month = {January},
type = {Preprint} }
A Galerkin-Newton-ADI Method for Solving Large-Scale Algebraic Riccati Equations;
Benner, Peter; Saak, Jens;
2010.
SPP1253 preprint SPP1253-090.
@TECHREPORT{KoeS09,
author = {Martin K\"ohler and Jens Saak},
title = {Efficiency improving implementation techniques for large scale matrix equation solvers},
institution = {TU Chemnitz},
year = 2009,
type = {{C}hemnitz {S}cientific {C}omputing {P}rep.},
number = {CSC 09-10},
type = {Preprint} }
Efficiency improving implementation techniques for large scale matrix equation solvers;
Köhler, Martin; Saak, Jens;
CSC Preprint 09-10;
2009.
@PhdThesis{Saa09,
author = {Jens Saak},
title = {Efficient Numerical Solution of Large Scale Algebraic Matrix Equations in PDE Control and Model Order Reduction},
school = {TU Chemnitz},
year = 2009,
month = {July},
note = {available from \url{http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200901642}} }
Efficient Numerical Solution of Large Scale Algebraic Matrix Equations in PDE Control and Model Order Reduction;
Saak, Jens;
PhD Thesis, TU Chemnitz; 2009.
@ARTICLE{BMS08,
author = {P. Benner and H. Mena and J. Saak},
title = {On the Parameter Selection Problem in the {N}ewton-{ADI} Iteration for Large-Scale {R}iccati Equations},
journal = {Electronic Transitions on Numerical Analysis},
year = {2008},
volume = {29},
pages = {136-149},
booktitle = {Special Volume on Applied Linear Algebra},
comment = {ISSN 1068-9613},
publisher = {ETNA},
series = {Electronic Transitions on Numerical Analysis} }
On the Parameter Selection Problem in the Newton-ADI Iteration for Large-Scale Riccati Equations;
Benner, Peter; Mena, Hermann; Saak, Jens;;
Electronic Transactions on Numerical Analysis  :  Vol. 29 of ETNA pp. 136-149;
2008. ISBN/ISSN: 1068-9613
also available as CSC Preprint 06-03 .
@Article{BenS08,
author = {Benner,
Peter and Saak,
Jens},
title = {Efficient solution of large scale Lyapunov and Riccati equations arising in model order reduction problems},
journal = {Proc. Appl. Math. Mech.},
year = {2008},
month = {December},
volume = 8,
number = 1 }
Efficient solution of large scale Lyapunov and Riccati equations arising in model order reduction problems
Benner, Peter; Saak, Jens;
Proceedings in Applied Mathematics and Mechanics  :  
Wiley InterScience; 2008.
DOI: 10.1002/pamm.200810085.

Vorträge:

P. Kürschner
Low-rank residuals and new shift parameter strategies in ADI methods for large Lyapunov and Sylvester equations
XIII GAMM Workshop on Applied an Numerical Linear Algebra, Wuppertal, September 9-10, 2013

P. Kürschner
Recent numerical improvements in low-rank ADI methods
Numerical Analysis and Scientific Computation with Applications (NASCA13), Calais, France, June 24-26, 2013

J. Saak
Towards a GPU Add-On for the M.E.S.S.
XII GAMM Workshop on Applied an Numerical Linear Algebra, Chateau Liblice (CZ) , September 02-05, 2012

J. Saak
Numerische Lösung großer, dünn besetzter Matrix-Gleichungen zur Modellordnungsreduktion,
Regelungstechnisches Seminar, TU München, May 09, 2012

P. Kürschner
A completely real way of dealing efficiently with complex shifts in the low-rank ADI method,
GAMM 83nd Annual Scientific Conference, Darmstadt, March 26-30, 2012

J. Saak
On the Implementation of an Inexact Low Rank Kleinman-Newton Iteration for large and Sparse Riccati Equations,
GAMM ANLA Workshop on Matrix Equations and Tensor Techniques RWTH Aachen, December, 21-22,December, 21-22, 2011 2011

T. Breiten
On optimality of interpolation-based low-rank approximations of large-scale matrix equations,
GAMM Workshop on Workshop on Matrix Equations and Tensor Techniques, Aachen, December, 21-22, 2011

P. Kürschner
Efficient Handling of Complex Shift Parameters in the Low-rank Cholesky Factor ADI method,
Workshop on Matrix Equations and Tensor Techniques, Aachen, November 21 - 22, 2011, and GAMM Workshop 2011 on Applied and Numerical Linear Algebra, Bremen, September 22 - 23, 2011

M. Köhler
Solving Large Scale Matrix Equations on Multicore-CPUs;
17th ILAS Conference, Braunschweig, August 24, 2011

J. Saak
Acceleration of Newton-based Methods for Solving Large Sparse Algebraic Riccati Equations,
ILAS 2011, Braunschweig, August 23, 2011

J. Saak
Efficient solution of large scale Lyapunov and Riccati equations arising in model order reduction problems,
GAMM Jahrestagung 2008 Universität Bremen; March 31 - April 4, 2008

J. Saak
Efficient numerical solution of large scale matrix equations arising in LQR/LQG design for parabolic PDEs,
PDE Constrained Optimization - recent challenges and future developments Universität Hamburg; March 27-29, 2008

J. Saak
Efficient Implementation of Large Scale Lyapunov and Riccati Equation Solvers
Computational Methods with applications 2007; Harrachov (Czech Republic); August 20-25, 2007

J. Saak
ADI shift parameter computation for large scale algebraic Riccati and Lyapunov equations arising in the LQR problem for parabolic PDEs,
ALA2006 Düsseldorf; Heinrich Heine Universität Düsseldorf
Düsseldorf, July 23-27, 2006

J. Saak
On Adi Parameters For Solving PDE Control-related Matrix Equations,
GAMM Jahrestagung 2006; TU Berlin, Berlin, March 27-31, 2006




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Jens Saak, Martin Köhler, saak, koehlerm@mpi-magdeburg.mpg.de