@TECHREPORT{MPIMD10-02,
author = {Peter Benner, Tobias Breiten, Tobias Damm},
title = {Generalized Tangential Interpolation for Model Reduction of Discrete-Time MIMO Bilinear Systems},
number = {MPIMD/10-02},
month = dec,
year = 2010,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD11-02,
author = {Peter Benner, Tobias Breiten},
title = {Interpolation-Based ℋ₂-Model Reduction of Bilinear Control Systems},
number = {MPIMD/11-02},
month = jun,
year = 2011,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD11-04,
author = {Martin Stoll},
title = {One-shot solution of a time-dependent time-periodic PDE-constrained optimization problem},
number = {MPIMD/11-04},
month = jul,
year = 2011,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD11-06,
author = {Hermann Mena, Peter Benner},
title = {Rosenbrock methods for solving differential Riccati equations},
number = {MPIMD/11-06},
month = oct,
year = 2011,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD11-08,
author = {Peter Benner, Patrick Kürschner, Jens Saak},
title = {Efficient Handling of Complex Shift Parameters in the Low-Rank Cholesky Factor ADI method},
number = {MPIMD/11-08},
month = oct,
year = 2011,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD11-10,
author = {Peter Benner, Tobias Breiten},
title = {On optimality of interpolation-based low-rank approximations of large-scale matrix equations},
number = {MPIMD/11-10},
month = dec,
year = 2011,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD11-12,
author = {Thomas Mach, Jens Saak},
title = {Towards an ADI iteration for Tensor Structured Equations},
number = {MPIMD/11-12},
month = dec,
year = 2011,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD12-01,
author = {Peter Benner, Patrick Kürschner, Jens Saak },
title = {A Goal-Oriented Dual LRCF-ADI for Balanced Truncation},
number = {MPIMD/12-01},
month = jan,
year = 2012,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD12-03,
author = {Peter Benner, Tobias Breiten},
title = {Low rank methods for a class of generalized Lyapunov equations and related issues},
number = {MPIMD/12-03},
month = feb,
year = 2012,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD12-05,
author = {Peter Benner, Thomas Mach},
title = {The LR Cholesky Algorithm for Symmetric Hierarchical Matrices},
number = {MPIMD/12-05},
month = feb,
year = 2012,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD12-07,
author = {Christine Nowakowski, Patrick Kürschner, Peter Eberhard, Peter Benner},
title = {Model Reduction of an Elastic Crankshaft for Elastic Multibody Simulations},
number = {MPIMD/12-07},
month = mar,
year = 2012,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD12-09,
author = {Peter Benner, Matthias Voigt},
title = {Spectral Characterization and Enforcement of Negative Imaginariness for Descriptor Systems},
number = {MPIMD/12-09},
month = apr,
year = 2012,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD12-11,
author = {Peter Benner, Patrick Kürschner, Jens Saak},
title = {Real versions of low-rank ADI methods with complex shifts},
number = {MPIMD/12-11},
month = may,
year = 2012,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD12-13,
author = {Peter Benner, Hermann Mena},
title = {Numerical solution of the Infinite-Dimensional LQR-Problem and the associated Differential Riccati Equations},
number = {MPIMD/12-13},
month = aug,
year = 2012,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD12-15,
author = {Peter Benner, Grece El Khoury, Miloud Sadkane},
title = {On the Squared Smith Method for Large-Scale Stein Equations},
number = {MPIMD/12-15},
month = sep,
year = 2012,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD12-17,
author = {Martin W. Hess, Peter Benner},
title = {Fast Evaluation of Time-Harmonic Maxwell's Equations Using the
Reduced Basis Method},
number = {MPIMD/12-17},
month = oct,
year = 2012,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD12-19,
author = {Peter Benner, Jens Saak, Friedhelm Schieweck, Piotr Skrzypacz, Heiko K. Weichelt },
title = {A Non-Conforming Composite Quadrilateral Finite Element Pair for Feedback Stabilization of the Stokes Equations },
number = {MPIMD/12-19},
month = oct,
year = 2012,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD12-21,
author = {Henning Biermann, Sara Grundel, Denis Zorin},
title = {Subdivision schemes for surfaces with boundaries},
number = {MPIMD/12-21},
month = dec,
year = 2012,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD13-02,
author = {Xin Du, Peter Benner, Guanghong Yang, Dan Ye},
title = {Balanced Truncation of Linear Time-Invariant Systems at a Single Frequency},
number = {MPIMD/13-02},
month = jan,
year = 2013,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD13-04,
author = {Melina Freitag, Patrick Kürschner},
title = {Tuned preconditioners for inexact two-sided inverse and Rayleigh quotient iteration},
number = {MPIMD/13-04},
month = apr,
year = 2013,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD13-06,
author = {Peter Benner, Tatjana Stykel},
title = {Numerical Solution of Projected Algebraic Riccati Equations},
number = {MPIMD/13-06},
month = may,
year = 2013,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD13-08,
author = {Martin Stoll, Tobias Breiten},
title = {A low-rank in time approach to PDE-constrained optimization},
number = {MPIMD/13-08},
month = jun,
year = 2013,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD13-10,
author = {Hamdullah Yücel, Martin Stoll, Peter Benner},
title = {A Discontinous Galerkin Method for Optimal Control Problems Governed by a System of Convection-Diffusion PDEs with Nonlinear Reaction Terms},
number = {MPIMD/13-10},
month = jul,
year = 2013,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD13-12,
author = {Peter Benner, Vasile Sima, Matthias Voigt},
title = {FORTRAN 77 Subroutines for the Solution of Skew-Hamiltonian/Hamiltonian Eigenproblems - Part II: Implementation and Numerical Results},
number = {MPIMD/13-12},
month = jul,
year = 2013,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD13-14,
author = {Peter Benner, Serkan Gugercin, Karen Willcox},
title = {A Survey of Model Reduction Methods for Parametric Systems},
number = {MPIMD/13-14},
month = aug,
year = 2013,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD13-16,
author = {Hamdullah Yücel, Peter Benner},
title = {Adaptive discontinuous Galerkin methods for state constrained optimal control problems governed by convection diffusion equations},
number = {MPIMD/13-16},
month = sep,
year = 2013,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD13-18,
author = {Peter Benner, Patrick Kürschner, Jens Saak},
title = {Self-Generating and Efficient Shift Parameters in ADI Methods for Large Lyapunov and Sylvester Equations},
number = {MPIMD/13-18},
month = oct,
year = 2013,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD13-20,
author = {Ryan Lowe, Matthias Voigt},
title = {L_∞-Norm Computation for Large-Scale Descriptor Systems Using Structured Iterative Eigensolvers},
number = {MPIMD/13-20},
month = oct,
year = 2013,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD13-22,
author = { Björn Baran, Martin Köhler, Nitin Prasad, 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/}},
}

@TECHREPORT{MPIMD13-24,
author = {Peter Benner, Philip Losse, Volker Mehrmann, Matthias Voigt},
title = {Numerical Solution of Eigenvalue Problems for Alternating Matrix Polynomials and Their Application in Control Problems for Descriptor Systems},
number = {MPIMD/13-24},
month = dec,
year = 2013,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD14-02,
author = {Tobias Breiten, Valeria Simoncini, Martin Stoll},
title = {Fast iterative solvers for fractional differential equations},
number = {MPIMD/14-02},
month = jan,
year = 2014,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD14-04,
author = {Peter Benner, Jan Heiland},
title = {LQG-Balanced Truncation Low-Order Controller for Stabilization of Laminar Flows},
number = {MPIMD/14-04},
month = mar,
year = 2014,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD14-06,
author = {Peter Benner, Steffen Börm, Thomas Mach, Knut Reimer},
title = {Computing the Eigenvalues of Symmetric $H2$-Matrices by Slicing the Spectrum},
number = {MPIMD/14-06},
month = mar,
year = 2014,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD14-08,
author = {Peter Benner, Hermann Mena, René Schneider},
title = {Modeling Glyphosate Aerial Spray Drift at the Ecuador-Colombia Border},
number = {MPIMD/14-08},
month = apr,
year = 2014,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD14-10,
author = {Jessica Bosch,, Martin Stoll},
title = {Preconditioning for vector-valued Cahn--Hilliard equations},
number = {MPIMD/14-10},
month = jun,
year = 2014,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD14-12,
author = {Peter Benner, Patrick Kürschner, Zoran Tomljanović, Ninoslav Truhar},
title = {Semi-active damping optimization of vibrational systems using the parametric dominant pole algorithm},
number = {MPIMD/14-12},
month = jul,
year = 2014,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD14-14,
author = {Norman Lang, Hermann Mena, Jens Saak},
title = {On the benefits of the LDL^T factorization for large-scale differential matrix equation solvers},
number = {MPIMD/14-14},
month = jul,
year = 2014,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD14-16,
author = {Martin Redmann, Peter Benner},
title = {Approximation and Model Order Reduction for Second Order Systems with Levy-Noise},
number = {MPIMD/14-16},
month = sep,
year = 2014,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD14-18,
author = {Christopher Beattie, Peter Benner},
title = {ℋ₂-Optimality Conditions for Structured Dynamical Systems},
number = {MPIMD/14-18},
month = oct,
year = 2014,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD14-20,
author = {Peter Benner, Jens Saak, M. Monir Uddin},
title = {Balancing based model reduction for structured index-2 unstable descriptor systems with application to flow control },
number = {MPIMD/14-20},
month = nov,
year = 2014,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD14-22,
author = {Yongjin Zhang, Lihong Feng, Suzhou Li, Peter Benner},
title = {An efficient output error bound for model order reduction of parametrized evolution equations},
number = {MPIMD/14-22},
month = dec,
year = 2014,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD14-24,
author = {Julie Eaton, Sara Grundel, Mert Gürbüzbalaban, Michael Overton},
title = {Polynomial Root Radius Optimization with Affine Constraints},
number = {MPIMD/14-24},
month = dec,
year = 2014,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD15-01,
author = {Ulrike Baur, Peter Benner, Bernard Haasdonk, Christian Himpe, Immanuel Maier, Mario Ohlberger},
title = {Comparison of methods for parametric model order reduction of instationary problems},
number = {MPIMD/15-01},
month = feb,
year = 2015,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD15-03,
author = {Peter Benner, Jan Heiland},
title = {Time-dependent Dirichlet Conditions in Finite Element Discretizations},
number = {MPIMD/15-03},
month = mar,
year = 2015,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD15-05,
author = {Peter Benner, Akwum Onwunta, Martin Stoll},
title = {Block-diagonal preconditioning for optimal control problems constrained by PDEs with uncertain inputs},
number = {MPIMD/15-05},
month = apr,
year = 2015,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD15-07,
author = {Pawan Goyal, Mian Ilyas Ahmad, Peter Benner},
title = {Krylov Subspace-based Model Reduction for a Class of Bilinear Descriptor Systems},
number = {MPIMD/15-07},
month = may,
year = 2015,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD15-09,
author = {Peter Benner, Patrick Kürschner, Jens Saak},
title = {Frequency-Limited Balanced Truncation with Low-Rank Approximations},
number = {MPIMD/15-09},
month = jul,
year = 2015,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD15-11,
author = {Hamdullah Yücel, Martin Stoll, Peter Benner},
title = {Adaptive Discontinuous Galerkin Approximation of Optimal Control Problems Governed by Transient Convection-Diffusion Equations},
number = {MPIMD/15-11},
month = jul,
year = 2015,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD15-13,
author = {Peter Benner, Hamdullah Yücel},
title = {Adaptive Symmetric Interior Penalty Galerkin method for boundary control problems},
number = {MPIMD/15-13},
month = aug,
year = 2015,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD15-15,
author = {Sergey Dolgov, Martin Stoll},
title = {Low-rank solutions to an optimization problem constrained by the Navier-Stokes equations},
number = {MPIMD/15-15},
month = sep,
year = 2015,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD15-17,
author = {Lihong Feng, Athanasios C. Antoulas, Peter Benner},
title = {Some a posteriori error bounds for reduced order modelling of (non-)parametrized linear systems},
number = {MPIMD/15-17},
month = oct,
year = 2015,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD15-19,
author = {Peter Benner, Tatjana Stykel},
title = {Model Order Reduction for Differential-Algebraic Equations: a Survey},
number = {MPIMD/15-19},
month = nov,
year = 2015,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD15-21,
author = {Mian Ilyas Ahmad, Ulrike Baur, Peter Benner},
title = {Implicit Volterra Series Interpolation for Model Reduction of Bilinear Systems},
number = {MPIMD/15-21},
month = dec,
year = 2015,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD16-01,
author = {Peter Benner, Jonas Denißen, Ludwig Kohaupt},
title = {Trigonometric spline and spectral bounds for the solution of linear time-periodic systems},
number = {MPIMD/16-01},
month = jan,
year = 2016,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}

@TECHREPORT{MPIMD17-01,
author = {Tobias Keßler, Christian Kunde, Nick Mertens, Dennis Michaels, Achim Kienle},
title = {Global Optimization of Distillation Columns using Surrogate Models},
number = {MPIMD/17-01},
month = may,
year = 2017,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}