Papers/Veröffentlichungen

Papers by / co-authored by Heike Faßbender Eigene und beteiligte Arbeiten von Heike Faßbender

Modellreduktion -- Eine systemtheoretisch orientierte Einführung
Peter Benner, Heike Faßbender
Springer Studium Mathematik (Master) 2024, https://doi.org/10.1007/978-3-662-67493-2

A note on the singular value decomposition of idempotent and involutory matrices
Heike Faßbender, Martin Halwaß
Preprint arxiv:2403.05214

A class of Petrov-Galerkin Krylov methods for algebraic Riccati equations (previous title: A rational Krylov subspace based projection method for solving large-scale algebraic Riccati equations via low-rank approximations)
Christian Bertram, Heike Faßbender
Electronic Transactions on Numerical Analysis (ETNA) 62, pp. 138–162, 2024, doi.org/10.1553/etna_vol62s138
Preprint arxiv:2312.08855

On a family of low-rank algorithms for large-scale algebraic Riccati equations
Christian Bertram, Heike Faßbender
Linear Algebra and its Applications 687, pp. 38-67, 2024
Preprint arxiv:2304.01624

Concept for thermal analysis of batteries using reduced order modeling
Anna Szardenings, Niels Petersen, Heike Faßbender - AIP Conference Proceedings, 2022

The Hamiltonian Extended Krylov Subspace Method
Peter Benner, Heike Faßbender, Michel-Niklas Senn
Preprint arXiv:2202.12640
Electronic Journal of Linear Algebra 38, 572-606, 2022, DOI: 10.13001/ela.2022.6977

Model Reduction of Complex Dynamical Systems
Editors: Peter Benner, Tobias Breiten, Heike Faßbender, Michael Hinze, Tatjana Stykel, Ralf Zimmermann
Int. Series Numerical Math. (ISNM) Volume 171, Birkhäuser 2021

A rational Even-IRA algorithm for the solution of T-even polynomial eigenvalue problems
Peter Benner, Heike Faßbender, Philip Saltenberger
SIAM J. Matrix Anal. Appl., 42(3), 1172–1198, 2021 (https://doi.org/10.1137/20M1364485)
see also Preprint arxiv:2009.01762

Riccati ADI: Existence, uniqueness and new iterative methods
Christian Bertram, Heike Faßbender
Preprint arXiv:2004.11212

Nearly optimal scaling in the SR decomposition
Heike Faßbender, Miroslav Rozloznik, Sanja Singer
Preprint arXiv:2004.03288
Linear Algebra and its Applications 2020, https://doi.org/10.1016/j.laa.2020.11.011

A link between gramian based model order reduction and moment matching
Christian Bertram, Heike Faßbender
In: Benner P., Breiten T., Faßbender H., Hinze M., Stykel T., Zimmermann R. (eds) Model Reduction of Complex Dynamical Systems. International Series of Numerical Mathematics, vol 171. Birkhäuser, Cham.
see also Preprint arXiv:2003.03101

On normal and structured matrices under unitary structure-preserving transformations
Erna Begovic Kovac, Heike Faßbender, Philip Saltenberger
Preprint arXiv:1810.03369v2
Linear Algebra and its Applications, 608, pp. 322-342, 2021, https://doi.org/10.1016/j.laa.2020.09.019

Simultaneous hollowisation, joint numerical range, and stabilization by noise
Tobias Damm, Heike Faßbender
Preprint arXiv:1910.08813
SIAM Matrix Analysis and its Applications Vol. 41, Issue 2, p. 637-656, 2020, DOI: 10.1137/19M1294265

A note on the singular value decomposition of (skew-)involutory and (skew-)coninvolutory matrices
Heike Faßbender, Martin Halwaß
Preprint arXiv:1905.11106
Special Matrices Volume 8 (2020)
Correction: In Line 8/9 on Page 9 of the published version of the paper it should read "Each $2 \times 2$ block can be diagonalized. Thus, Theorem 6 yields that any involutory matrix is diagonalizable to ...".

A quadrature framework for solving Lyapunov and Sylvester equations
Christian Bertram, Heike Faßbender
Preprint arXiv:1903.05383
Linear Algebra and its Applications 622, S. 66--103, 2021, DOI: 10.1016/j.laa.2021.03.029

On a modification of the EVEN-IRA algorithm for the solution of T-even polynomial eigenvalue problems
Heike Faßbender, Philip Saltenberger
Proceedings in Applied Mathematics and Mechanics (PAMM) 18(1), 2018

Some remarks on the complex J-symmetric eigenproblem
Peter Benner, Heike Faßbender, Chao Yang
Linear Algebra and its Applications 544, pp. 407-442, 2018,
see also Max Planck Institute Magdeburg Preprint MPIMD/15-12, 2015

A Revised Moment Error Expression for the AIRGA Algorithm
Heike Faßbender, Julius Mayer
Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica, Vol. 26(2), pp. 87-104, 2018.

Block-Kronecker Ansatz Spaces for Matrix Polynomials
Heike Faßbender, Philip Saltenberger
Linear Algebra and its Applications 542, pp. 118-148, 2018,
see also On a new kind of Ansatz Spaces for Matrix Polynomials, Preprint 2016 arXiv:1610.05988

On vector spaces of linearizations for matrix polynomials in orthogonal bases
Heike Faßbender, Philip Saltenberger
Linear Algebra and its Applications 525, pp. 59-83, 2017, Preprint 2016 arXiv:1609.09493

Symmetric and skew-symmetric block-Kronecker linearizations
Heike Faßbender, Javier Perez Alvaro, Nikta Shayanfar
Preprint 2016 arXiv:1606.01766

Some Notes on the Linearization of Matrix Polynomials in Standard and Tschebyscheff Basis
Heike Faßbender, Philip Saltenberger
Preprint 2016

A sparse linearization for Hermite interpolation matrix polynomials
Heike Faßbender, Javier Perez Alvaro, Nikta Shayanfar
MIMS Preprint 2015.98

Birkhoff polynomial basis
Amir Amiraslani, Heike Faßbender, Nikta Shayanfar
In: Bebiano N. (eds), 'Applied and Computational Matrix Analysis. MAT-TRIAD 2015', Springer Proceedings in Mathematics & Statistics 192, 2017, pp. 1-26.

On the conditioning of factors in the SR decomposition
Heike Faßbender, Miro Rozloznik
Linear Algebra and its Applications 505,pp. 224 - 244, 2016

On the diagonalizability of a matrix by symplectic equivalence, similarity or congruence transformations
Ralph John De La Cruz, Heike Faßbender
Linear Algebra and its Applications, Vol. 496, pp. 288-306, 2016.

A fully adaptive rational global Arnoldi method for the model-order reduction of second-order MIMO systems with proportional damping
Thomas Bonin, Heike Faßbender, Andreas Soppa, Michael Zäh
Mathematics and Computers in Simulation, Volume 22, pp. 1 -19, 2016

Breaking Van Loan's Curse: A Quest for Structure-Preserving Algorithms for Dense Structured Eigenvalue Problems
Angelika Bunse-Gerstner, Heike Faßbender
in Benner, Bollhöfer, Kressner, Mehl, Stykel (Eds.), Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory, Springer ISBN 978-3-319-15259-2 , pp. 3 - 23, 2015
Model Order Reduction: Techniques and Tools
Peter Benner, Heike Faßbender
in Baillieul, Samad(Eds.), Encyclopedia of Systems and Control, Springer ISBN 978-1-4471-5057-2 (Online),pp. 1 -- 10, 2014
Structured Eigenvalue Problems - Structure-Preserving Algorithms, Structured Error Analysis
in Handbook of Linear Algebra, Second Edition, CRC Press, Taylor and Francis Group, Chapter 63, 22 Seiten, 2014.
Model Order Reduction for Steady Aerodynamics of High-Lift Configurations
Alexander Vendl, Heike Faßbender, Stefan Görtz, Ralf Zimmermann, Michael Mifsut
CEAS Aeronautical Journal, Volume 5, Issue 4, pp. 487 - 500, 2014.
Model Order Reduction for Unsteady Aerodynamic Applications
Alexander Vendl, Heike Faßbender
Proceedings in Applied Mathematics and Mechanics (PAMM) 13(1), pp. 475 - 476, 2013.
Projection-Based Model Order Reduction for Steady Aerodynamics
Alexander Vendl, Heike Faßbender
in "Computational Flight Testing - Results of the Closing Symposium of the German Research Initiative ComFliTe, Braunschweig, Germany, June 11st-12th, 2012", Springer Series Notes on Numerical Fluid Mechanics and Multidisciplinary Design, Vol. 123, Kroll, N.; Radespiel, R.; Burg, J.W.; Sørensen, K. (Eds.), pp. 151 - 166, 2013
More Simulation -- Less Testing
in T. Lery, H. Tewkesbury, M. Primicerio, M. J. Esteban, M. Fontes, Y. Maday, V. Mehrmann, G. Quadros, W. Schilders, A. Schuppert (Eds.), European Success Stories in Industrial Mathematics, p. 88, Springer 2012.
Modellreduktion - mehr Simulation, weniger teure Prototypentests (in German)
in Facettenreiche Mathematik - Einblicke in die moderne mathematische Forschung für alle, die mehr von Mathematik verstehen wollen, pp. 89 - 110, Springer 2011.
Efficient POD-based Model Order Reduction for Steady Aerodynamic Applications
Alexander Vendl, Heike Faßbender
in C. Poloni, D. Quagliare, J. Periaux, N. Gauger, and K. Giannakoglou, editors, Evolutionary and deterministic methods for design, optimization and control, pages 296 - 309, CIRA, Capua, Italy, 2011. EUROGEN 2011.
Missing Point Estimation for Steady Aerodynamic Applications
Alexander Vendl, Heike Faßbender
Proceedings in Applied Mathematics and Mechanics (PAMM) 11(1), pp. 839 - 840, 2011.
Einsatz moderner Ordnungsreduktionsverfahren - Neue Wege für die numerische Simulation von Werkzeugmaschinen (in German)
Thomas Bonin, Michael Zäh, Andreas Soppa, Heike Faßbender,
wt-online, 3-2011, pp. 150 - 155, 2011.
Moderne Modellordnungsreduktionsverfahren für Finite-Elemente-Modelle zur Simulation von Werkzeugmaschinen (in German)
Thomas Bonin, Andreas Soppa, Jens Saak, Michael Zäh, Heike Faßbender, Peter Benner, in T. Bertram and B. Corves (Eds.), Tagungsband der VDI-Fachtagung Mechatronik 2011, 31.3-1.4.2011, Dresden, pp. 333 - 338, TU Dresden, 2011.
Machine tool simulation based on reduced order FE models
Heike Faßbender and Andreas Soppa
Mathematics and Computers in Simulation, Vol 82, pp. 404 - 413, 2011.
Time dependent weight functions for the Trajectory Piecewise-Linear approach?
Juan Pablo Amorocho, Heike Faßbender
Report 2011.
On the numerical solution of large-scale sparse discrete-time Riccati equations
Peter Benner, Heike Faßbender
Advances in Computational Mathematics 35(2), pp. 119 - 147, 2011
(see also Chemnitz Scientific Computing Preprints 09-11, TU Chemnitz, December 2009).
A Hamiltonian Krylov-Schur-type method based on the symplectic Lanczos method
Peter Benner, Heike Faßbender and Martin Stoll
Linear Algebra and its Applications 435, pp. 578 - 600, 2011
(see also Report Number 09/32, Oxford Center for Collaborative Applied Mathematics (OCCAM), Oxford, England).
Wie wird die Nachhaltigkeit des Qualitätsmanagements sichergestellt? (in German)
Jule Bobzin, Heike Faßbender, Christiane Miosge
in Mathias Winde (Hrsg.), Von der Qualitätsmessung zum Qualitätsmanagement, Stifterverband für die Deutsche Wissenschaft, pp. 36 - 46, 2010.
Technische Universität Braunschweig -- Hervorragende Qualität und viel Raum für eigene Ideen (in German)
Heike Faßbender, Christiane Miosge
in Mathias Winde (Hrsg.), Von der Qualitätsmessung zum Qualitätsmanagement, Stifterverband für die Deutsche Wissenschaft, pp. 48 - 57, 2010.
Some contributions to the model order reduction of large scale non-linear electric circuits
Juan Pablo Amorocho, Heike Faßbender
Proceedings in Applied Mathematics and Mechanics (PAMM) 10(1), pp. 639 - 640, 2010.
Proper Orthogonal Decomposition for steady aerodynamic applications
Alexander Vendl, Heike Faßbender
Proceedings in Applied Mathematics and Mechanics (PAMM) 10(1), pp. 635 - 636, 2010.
Quadratically normal and congruence-normal matrices
Heike Faßbender and Khakim D. Ikramov
Journal of Mathematical Sciences, Vol. 165, No. 5, pp. 521 - 532, 2010
(see also Zapiski nauchnych seminarov POMI, Vol. 367, pp. 45 - 66, 2009 (in Russian)).
Novel Model Reduction Techniques for Control of Machine Tools
Peter Benner, Thomas Bonin, Heike Faßbender, Jens Saak, Andreas Soppa, Michael F. Zäh,
Proceedings of the ANSYS Conference & 27. CADFEM Users' Meeting 2009, 18.-20. November 2009, Congress Center Leipzig, paper 2.9.18 (10 pages), 2009.
Modale versus moderne Ordnungsreduktionsverfahren: Effiziente Simulation von Werkzeugmaschinen (in German)
Thomas Bonin, Michael F. Zäh, Andreas Soppa, Heike Faßbender, Jens Saak, and Peter Benner
MECHATRONIK, Vol. 11-12/2009, pp. 46 - 47, 2009.
Machine tool simulation based on reduced order FE models
Heike Faßbender and Andreas Soppa
proceedings paper in I. Troch; F. Breitenecker: No. 35 Vol. 2 of ARGESIM-Reports; 2009.
revised version
Solving Large-Scale Quadratic Eigenvalue Problems with Hamiltonian eigenstructure using a Structure-Preserving Krylov Subspace Method
Peter Benner, Heike Faßbender and Martin Stoll
Electronic Transactions on Numerical Analysis Vol 29, pp. 212 - 229, 2008.
A note on the product of two skew-Hamiltonian matrices and the product of two skew-symmetric matrices
Heike Faßbender and Khakim D. Ikramov
Journal of Mathematical Sciences, Vol. 157, No. 5, pp. 697 - 700, 2009
(see also Zapiski nauchnych seminarov POMI, Vol. 359, pp. 45-51, 2008 (in Russian)).
Structured polynomial eigenproblems related to time delay systems
Heike Faßbender, D.S. Mackey, N. Mackey and C. Schröder
Electronic Transactions on Numerical Analysis Vol 31, pp. 306 - 330, 2008
(see also Extended version of 'Structured polynomial eigenproblems related to time delay systems').
Some properties of generalized K-centrosymmetric H-Matrices
Heike Faßbender and Zhongyun Liu
Journal of Computational and Applied Mathematics Vol. 215, Issue 1, pp. 38 - 48, 2008.
Conjugate-normal matrices: a survey
Heike Faßbender and Khakim D. Ikramov
Linear Algebra and its Applications, 429(7), pp. 1425 - 1441, 2008.
A note on an unusual type of polar decomposition
Heike Faßbender and Khakim D. Ikramov
Linear Algebra and its Applications, 429(1), pp. 42 - 49, 2008.
Simultaneous reduction to a block triangular form by a unitary congruence transformation
Heike Faßbender and Khakim D. Ikramov
Journal of Mathematical Sciences, Vol. 150, No. 2, pp. 1943 - 1950, 2008
(see also Zapiski nauchnych seminarov POMI, Vol. 346, pp. 49 - 62, 2007 (in Russian)).
Numerische Lineare Algebra -- Heute notwendiger denn je! (in German)
Heike Faßbender
Rundbrief GAMM 2/2007, pp.36 - 39, 2007.
Strategies for Parallelizing the Solution of Rational Matrix Equations
José M. Badía, Peter Benner, Maribel Castillo, Heike Faßbender, Rafael Mayo, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí
in C. Bischof, M. Bücker, P. Gibbon, G.R. Joubert, T. Lippert, B. Mohr, and F. Peters (editors), Parallel Computing: Architectures, Algorithms and Applications. Proceedings of the International Conference ParCo 2007, NIC Series Volume 38, pp. 255 - 262, John von Neumann-Institut für Computing, Jülich, Germany, 2007.
On the solution of the rational matrix equation X = Q + LX^{-1}L^T method
Heike Faßbender and Peter Benner
EURASIP Journal on Applied Signal Processing, vol. 2007, Article ID 21850, 10 pages, 2007
(see also Chemnitz Scientific Computing Preprint CSC/06-02, 2006).
The Parameterized SR Algorithm for Hamiltonian Matrices
Heike Faßbender
Electronic Transactions on Numerical Analysis Vol 26, pp. 121 - 145, 2007.
Some observations on the Youla form and conjuagte-normal matrices
Heike Faßbender and Khakim D. Ikramov
Linear Algebra and its Applications, 422(1), pp. 29 - 38, 2007.
An inverse eigenvalue problem and an associated approximation problem for generalized K-centrohermitian matrices
Heike Faßbender and Zhongyun Liu
Journal of Computational and Applied Mathematics Vol. 206, Issue 1, pp. 578 - 585, 2007.
A detailed derivation of the parameterized SR algorithm and the symplectic Lanczos method for Hamiltonian matrices
Heike Faßbender
preprint 2006
Passivity preserving model reduction via a structured Lanczos method
Heike Faßbender and Peter Benner
Proceedings of the 2006 IEEE Conference on Computer-Aided Control Systems Design, Munich, Germany, October 4-6, 2006, pp. 8 - 13, IEEE 2006.
Numerische Methoden zur passivitätserhaltenden Modellreduktion (in German)
Heike Faßbender and Peter Benner
Automatisierungstechnik 54(4), pp. 153 - 160, 2006.
SYMMLQ-like procedure for Ax=b where A is a special normal matrix
Heike Faßbender and Khakim D. Ikramov
CALCOLO, Volume 43, Issue 1, pp 17 - 37, 2006.
Structured Eigenvalue Problems
Heike Faßbender and Daniel Kressner
GAMM Mitteilungen 29, No. 2, Themenheft Applied and Numerical Linear Algebra, Part II, pp. 297 - 318, 2006.
Several observations on symplectic, Hamiltonian, and skew-Hamiltonian matrices
Heike Faßbender and Khakim D. Ikramov
Linear Algebra and its Applications 400, pp. 15 - 29, 2005.
Computing matrix-vector products with centrosymmetric and centrohermitian matrices
Heike Faßbender and Khakim D. Ikramov
Linear Algebra and its Applications 364, pp. 235 - 241, 2003.
Computing roots of matrix products
Peter Benner and Heike Faßbender
ZAMM 81, Suppl. 3, pp. 717 - 718, 2001.
A Hybrid Method for the Numerical Solution of Discrete-Time Algebraic Riccati Equations
Peter Benner and Heike Faßbender
in V. Olshevsky, Structured Matrices in Mathematics, Computer Science, and Engineering, Vol. 1, Contemporary Mathematics, AMS, pp. 255 - 269, 2001.
Hamilton and Jacobi come full circle: Jacobi algorithms for structured Hamiltonian eigenproblems
Heike Faßbender, D. Steven Mackey and Niloufer Mackey
Linear Algebra and its Applications 332/334, pp. 37 - 80, 2001.
The Parameterized SR Algorithm for Symplectic (Butterfly) Matrices
Heike Faßbender
Mathematics of Computation 70, No. 236, pp. 1515 - 1541, 2001.
Cholesky-like Factorizations of Skew-Symmetric Matrices
Peter Benner, Ralph Byers, Heike Faßbender, Volker Mehrmann, David Watkins
Electronic Transactions on Numerical Analysis Vol. 11, pp. 85 - 93, 2000
(see also Preprint-Reihe des Chemnitzer SFB 393, Preprint SFB393/00-35).
An Implicitly Restarted Symplectic Lanczos Method for the Symplectic Eigenvalue Problem
Peter Benner and Heike Faßbender
SIAM Journal on Matrix Analysis and Applications 22, No. 3, pp. 682 - 713, 2000.
Error Analysis of the Symplectic Lanczos Method for the Symplectic Eigenvalue Problem
Heike Faßbender
BIT 40:3, pp. 471 - 496, 2000.
On the Perturbation Theory for the Unitary Eigenproblem
Birgit Bohnhorst, Angelika Bunse-Gerstner and Heike Faßbender
SIAM Journal on Matrix Analysis and Applications 21, No. 3, pp. 809 - 824, 2000.
Real and complex Hamiltonain square roots of skew-Hamiltonian matrices
D.S. Mackey, N. Mackey and Heike Faßbender
Mathematics & Statistics Report 92, 1999, Western Michigan University, Kalamazoo, USA. (This report is an updated version of Hamiltonian square roots of skew-Hamiltonian matrices, Linear Algebra and its Applications, v. 287, 1999. pp. 125 - 159.)
SLICOT drives tractors!
Peter Benner and Heike Faßbender
NICONET Report 1999-2, see also NICONET Newsletter 2, pp. 17 - 22, Januar 1999.
Initializing Newton's method for discrete-time algebraic Riccati equations using the butterfly SR algorithm
Peter Benner and Heike Faßbender
in O. Gonzalez (editor), Proceedings of the 1999 IEEE International Symposium on Computer Aided Control System Design, Kohala Coast-Island of Hawai'i, Hawai'i, USA, August 22-27, 1999, pp. 70 - 74.
SR and SZ algorithms for the symplectic (butterfly) eigenproblem
Peter Benner, Heike Faßbender and David Watkins
Linear Algebra and its Applications 287, pp. 41 - 76, 1999.
Hamiltonian Square Roots of Skew-Hamiltonian Matrices
Heike Faßbender, D. Steven Mackey, Niloufer Mackey and Hongguo Xu
Linear Algebra and its Applications 287, pp. 125 - 159, 1999.
On Sliding Window Schemes for Discrete Least-Squares Approximation by Trigonometric Polynomials
Heike Faßbender
Proceedings of the Fourth Institute of Mathematics Conference - Mathematics in Signal Processing, Oxford University Press 1998, pp. 315 - 326 (short version of Report 98-02, Berichte aus der Technomathematik).
The Symplectic Eigenvalue Problem, the Butterfly Form, the SR Algorithm, and the Lanczos Method
Peter Benner and Heike Faßbender
Linear Algebra and its Applications 275 - 276, pp. 19 - 47, 1998.
Error bounds in the isometric Arnoldi process
Angelika Bunse-Gerstner and Heike Faßbender
Journal of Computational and Applied Mathematics, Vol. 86, pp. 53 - 72, 1997.
Two Connections between the SR and HR Eigenvalue Algorithms
Peter Benner, Heike Faßbender and David Watkins
Linear Algebra and its Applications, Vol. 272, pp. 17 - 32, 1997.
Inverse Unitary Eigenproblems and Related Orthogonal Functions
Heike Faßbender
Numerische Mathematik, Vol. 77(3), pp. 323 - 345, 1997.
An Implicitly Restarted Symplectic Lanczos Method for the Hamiltonian Eigenvalue Problem
Peter Benner and Heike Faßbender
Linear Algebra and its Applications, Vol. 263, pp. 75 - 111, 1997
(see also A Restarted Symplectic Lanczos Method for the Hamiltonian Eigenvalue Problem,
Technical Report SPC 95_28, TU Chemnitz-Zwickau, 1995).
A Jacobi-like method for solving algebraic Riccati equations on parallel computers
Angelika Bunse-Gerstner and Heike Faßbender
IEEE Transactions on Automatic Control, Vol. 42, No 8, 1997.
On Numerical Methods for Discrete Least-Squares Approximation by Trigonometric Polynomials
Heike Faßbender
Mathematics of Computation, Vol. 66, No. 218, pp. 719 - 741, 1997.
A Note on Newbery's Algorithm for Discrete Least-Squares Approximation by Trigonometric Polynomials
Heike Faßbender
Electronic Transactions on Numerical Analysis, Vol. 4, pp. 64 - 74, 1996.
On Numerical Methods For Discrete Least-Squares Approximation By Trigonometric Polynomials
Heike Faßbender
Proceedings of the fifth SIAM conference on applied linear algebra, edited by J. Lewis, pp. 445 - 449, 1994.
On the generalized Schur decomposition of a matrix pencil for parallel computation
Angelika Bunse-Gerstner and Heike Faßbender,
SIAM J. Sci. Stat. Comp. 12, pp. 911 - 939, 1991.

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Papers by / co-authored by Heike Faßbender Eigene und beteiligte Arbeiten von Heike Faßbender

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