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# Peter Benner - Publications

## Books

 [B9] Model Reduction and Approximation: Theory and Algorithms Peter Benner, Albert Cohen, Mario Ohlberger, and Karen Willcox (Eds.) Computational Science and Engineering Vol. 15, SIAM Publications, Philadelphia, PA, 2017. [ISBN: 978-1-611974-81-2] DOI: 10.1137/1.9781611974829 [B8] Model Reduction of Parametrized Systems Peter Benner, Mario Ohlberger, Anthony Patera, Gianluigi Rozza, and Karsten Urban (Eds.) MS&A – Modeling, Simulation and Applications, Vol. 17, Springer International Publishing, 2017. [ISBN: 978-3-319-58785-1] DOI: 10.1007/978-3-319-58786-8 [B7] System Reduction for Nanoscale IC Design Peter Benner (Ed.) Mathematics in Industry, Vol. 20, Springer-Verlag, 2017. [ISBN: 978-3-319-07235-7 (hardcover), 978-3-319-07236-4 (eBook)] DOI: 10.1007/978-3-319-07236-4 [B6] Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory: Festschrift in Honor of Volker Mehrmann Peter Benner, Matthias Bollhöfer, Daniel Kressner, Christian Mehl, and Tatjana Stykel (Eds.) Springer International Publishing, 2015. [ISBN: 978-3-319-15259-2 (hardcover), ISBN: 978-3-319-15260-8 (eBook)] DOI: 10.1007/978-3-319-15260-8 [B5] Modelo para las aspersiones con glifosato: frontera Ecuador-Colombia [in Spanish] Peter Benner, Hermann Mena, and René Schneider Shaker-Verlag, Aachen, 2014. [ISBN: 978-3-8440-3061-7] DOI: 10.2370/9783844030617 [B4] Large-Scale Networks in Engineering and Life Sciences Peter Benner, Rolf Findeisen, Dietrich Flockerzi, Udo Reichl, and Kai Sundmacher (Eds.) Modeling and Simulation in Science, Engineering and Technology, Birkhäuser, Boston, MA, 2014. [ISBN: 978-3-319-08436-7 (hardcover), 978-3-319-08437-4 (eBook)] DOI: 10.1007/978-3-319-08437-4 [B3] Trends in PDE Constrained Optimization Günter Leugering, Peter Benner, Sebastian Engell, Andreas Griewank, Helmut Harbrecht, Michael Hinze, Rolf Rannacher, and Stefan Ulbrich (Eds.) International Series of Numerical Mathematics, Vol. 165, Birkhäuser, Basel, 2014. [ISBN: 978--3-319-05082-9 (hardcover), 978-3-319-05083-6 (eBook)] DOI: 10.1007/978-3-319-05083-6 [B2] Model Reduction for Circuit Simulation Peter Benner, Michael Hinze, and E. Jan W. ter Maten (Eds.) Lecture Notes in Electrical Engineering, Vol. 74, Springer-Verlag, 2011. [ISBN: 978-94-007-0088-8 (hardcover), 978-94-007-0090-1 (paperback)] Read online here. DOI: 10.1007/978-94-007-0089-5 [B1] Dimension Reduction of Large-Scale Systems Peter Benner, Volker Mehrmann, and Danny C. Sorensen (Eds.) Lecture Notes in Computational Science and Engineering, Vol. 45, Springer-Verlag, Berlin/Heidelberg, June 2005. [ISBN: 3-540-24545-6] DOI: 10.1007/3-540-27909-1

## Editorials

 [E15] Model Reduction of Complex Dynamical Systems - Editorial of the Special Issue corresponding to a Workshop held at SDU Odense, Denmark, January 11–13, 2017 Peter Benner, Heike Faßbender, Michael Hinze, Tatjana Stykel, and Ralf Zimmermann Advances in Computational Mathematics, Vol. 44, Issue 6, pp. 1687-1691, 2018. DOI: 10.1007/s10444-018-9640-6 [E14] 7th Workshop on Matrix Equations and Tensor Techniques Peter Benner, Heike Faßbender, Lars Grasedyck, Daniel Kressner, Beatrice Meini, and Valeria Simoncini Numerical Linear Algebra With Applications, Special Issue: 7th Workshop on Matrix Equations and Tensor Techniques, Vol. 25, Issue 6, e2223, 2018. DOI: 10.1002/nla.2223 [E13] Preface: Model Reduction of Parametrized Systems Gianluigi Rozza, Peter Benner, Mario Ohlberger, Anthony T. Patera, and Karsten Urban Model Reduction of Parametrized Systems, MS&A - Modeling, Simulation and Applications, Springer International Publishing, Cham, Vol. 17, pp. v-vi, 2017. DOI: 10.1007/978-3-319-58786-8 [E12] Preface: Model Reduction and Approximation: Theory and Algorithms Peter Benner, Albert Cohen, Mario Ohlberger, and Karen Willcox In P. Benner, A. Cohen, M. Ohlberger, and K. Willcox (Eds.) Model Reduction and Approximation: Theory and Algorithms, SIAM Publications, Philadelphia, PA, 2017. DOI: 10.1137/1.9781611974829 [E11] Preface: System Reduction for Nanoscale IC Design Peter Benner In P. Benner (Ed.), System Reduction for Nanoscale IC Design, Mathematics in Industry, Vol. 20, pp. v-vii, Springer International Publishing, Cham. 2017. DOI: 10.1007/978-3-319-07236-4 [E10] Model Order Reduction of Parameterized Systems (MoRePaS): Preface to the Special Issue of Advances in Computational Mathematics Peter Benner, Mario Ohlberger, Anthony T. Patera, Gianluigi Rozza, Danny C. Sorensen, and Karsten Urban Advances in Computational Mathematics, Vol. 41, Issue 5, pp. 955-960, 2015. DOI: 10.1007/s10444-015-9443-y [E9] Introduction to the special issue for EUCCO 2013 Peter Benner, Roland Herzog, Michael Hinze, Arnd Rösch, Anton Schiela, and Volker Schulz Computational Optimization and Applications, Vol. 62, No. 1, pp. 1-3, 2015. DOI: 10.1007/s10589-015-9776-y [E8] Preface: Festschrift in Honor of Volker Mehrmann Peter Benner, Matthias Bollhöfer, Daniel Kressner, Christian Mehl, and Tatjana Stykel In P. Benner, M. Bollhöfer, D. Kressner, Ch. Mehl, and T. Stykel (Eds.), Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory: Festschrift in Honor of Volker Mehrmann, pp. v-xvii, Springer International Publishing, 2015. [ISBN: 978-3-319-15259-2] DOI: 10.1007/978-3-319-15260-8 [E7] Introduction Günter Leugering, Andreas Griewank, Stefan Ulbrich, Helmut Harbrecht, Peter Benner, Rolf Rannacher, Michael Hinze, and Sebastian Engell In G. Leugering, P. Benner, S. Engell, A. Griewank, H. Harbrecht, M. Hinze, R. Rannacher, and S. Ulbrich (Eds.), Trends in PDE Constrained Optimization, International Series of Numerical Mathematics, Vol. 165, pp. 1-4, Springer International Publishing, Switzerland, 2014. [ISBN: 978-3-319-05082-9] DOI: 10.1007/978-3-319-05083-6_1 [E6] Introduction to Part III Adaptivity and Model Reduction Peter Benner and Rolf Rannacher In G. Leugering, P. Benner, S. Engell, A. Griewank, H. Harbrecht, M. Hinze, R. Rannacher, and S. Ulbrich (Eds.), Trends in PDE Constrained Optimization, International Series of Numerical Mathematics, Vol. 165, pp. 249-250, Springer International Publishing, Switzerland, 2014. [ISBN: 978-3-319-05082-9] DOI: 10.1007/978-3-319-05083-6_16 [E5] Structured Matrix Computations in Non-Euclidean Geometries: Algorithms and Applications Peter Benner, Miloud Sadkane, and Ahmed Salam BIT Numerical Mathematics, Vol. 54, No. 1, pp. 1-5, 2014. DOI: 10.1007/s10543-014-0479-z. [E4] Preface of the Guest-Editors Peter Benner and Daniel Kressner GAMM Mitteilungen, Vol. 36, No. 1, pp. 6-7, 2013. DOI: 10.1002/gamm.201310001. [E3] A Mathematical Biography of Danny C. Sorensen Peter Benner, Mark Embree, Richard B. Lehoucq, and C.T. Kelley Linear Algebra and its Applications, Vol. 436, Issue 8, pp. 2717-2724, 2012. DOI: 10.1016/j.laa.2012.01.031. [E2] Editorial: Large-Scale Matrix Equations of Special Type Peter Benner Numerical Linear Algebra with Applications, Vol. 15, No. 9, pp. 747-754, 2008. DOI: 10.1002/nla.621. [E1] Preface Special Issue on "Order reduction of large-scale systems" Peter Benner, Roland W. Freund, Danny C. Sorensen, and Andras Varga Linear Algebra and its Applications, Vol. 415, Issues 2-3, pp. 231-234, 2006. DOI: 10.1016/j.laa.2006.01.018.

## Submitted articles

 [S34] An Adaptive Pole-Matching Method for Interpolating Reduced-Order Models Yao Yue, Lihong Feng, and Peter Benner Submitted, July 2019. [S33] Model Order Reduction for Bilinear Control Systems with Inhomogeneous Initial Conditions Xingang Cao, Peter Benner, Igor Pontes Duff, and Wil Schilders Submitted, July 2019. [S32] Model Order Reduction for Delay Systems by Iterative Interpolation Dominik Alfke, Giulio Antonini, Peter Benner, Lihong Feng, and Luigi Lombardi Submitted, July 2019. [S31] Low-Rank Linear Fluid-Structure Interaction Discretizations Roman Weinhandl, Peter Benner, and Thomas Richter arXiv Preprint arXiv:1905.11000, [math.NA], May 2019. [S30] A Subspace Framework for H∞-Norm Minimization Nicat Aliyev, Peter Benner, Emre Mengi, and Matthias Voigt arXiv Preprint arXiv:1905.04208, [math.NA], May 2019. [S29] New Error Estimator for Reduced-order Modeling of Linear Parametric Systems Lihong Feng and Peter Benner Submitted, May 2019. [S28] Reduced Models and Uncertainty Quantification Yao Yue, Lihong Feng, Peter Benner, Roland Pulch, Sebastian Schöps Submitted, April 2019. [S27] Sparse (P)MOR for Electro-Thermal Coupled Problems with Many Inputs Nicodemus Banagaaya, Lihong Feng, and Peter Benner Submitted, April 2019. [S26] Parametric Model Order Reduction for Electro-Thermal Coupled Problems Lihong Feng and Peter Benner Submitted, April 2019. [S25] Interpolation-Based Model Order Reduction for Polynomial Parametric Systems Peter Benner and Pawan Goyal arXiv Preprint arXiv:1904.11891, [math.NA], April 2019. [S24] Computing Electrostatic Potentials using Regularization based on the Range-Separated Tensor Format Peter Benner, Venera Khoromskaia, Boris Khoromskij, Cleophas Kweyu, and Matthias Stein arXiv Preprint arXiv:1901.09864, [math.NA], January 2019. [S23] Model Order Reduction of Linear Switched Systems with Constrained Switching Ion Victor Gosea, Igor Pontes Duff, Peter Benner and Athanasios C. Antoulas Revised December 2018. [S22] Hankel-Norm Approximation of Large-Scale Descriptor Systems Peter Benner and Steffen W. R. Werner arXiv Preprint arXiv:1612.06205v2, [math.OC], December 2018. [S21] Computational Experience with a Modified Newton Solver for Discrete-time Algebraic Riccati Equations Vasile Sima and Peter Benner Submitted, November 2018. [S20] Solution Formulas for Differential Sylvester and Lyapunov Equations Maximilian Behr, Peter Benner, and Jan Heiland arXiv Preprint arXiv:1811.08327[math.NA], November 2018. [S19] A Numerical Comparison of Solvers for Large-Scale, Continuous-Time Algebraic Riccati Equations Peter Benner, Zvonimir Bujanović, Patrick Kürschner, and Jens Saak arXiv Preprint arXiv:1811.00850[math.NA], November 2018. [S18] A Stochastic Maximum Principle for Control Problems Constrained by the Stochastic Navier-Stokes Equations Peter Benner and Christoph Trautwein arXiv Preprint arXiv:1810.12119[math.OC], October 2018. [S17] On the Existence and Uniqueness of the Solution of a Parabolic Optimal Control Problem with Uncertain Inputs Peter Benner, Akwum Onwunta, and Martin Stoll arXiv Preprint arXiv:1809.10645[math.OC], September 2018. [S16] Cross-Gramian-Based Dominant Subspaces Peter Benner and Christian Himpe arXiv Preprint arXiv:1809.08066[math.OC], September 2018. [S15] Greedy Low-Rank Algorithm for Spatial Connectome Regression Patrick Kürschner, Sergey Dolgov, Kameron Decker Harris, and Peter Benner arXiv Preprint arXiv:1808.05510[math.NA], August 2018. [S14] Peer Methods for the Solution of Large-Scale Differential Matrix Equations Peter Benner and Norman Lang arXiv Preprint arXiv:1807.08524 [math.NA], July 2018. [S13] Efficient Numerical Methods for Gas Network Modeling and Simulation Yue Qiu, Sara Grundel, Martin Stoll, and Peter Benner arXiv Preprint arXiv:1807.07142 [math.NA], July 2018. [S12] Efficient Solution of Large-Scale Algebraic Riccati Equations Associated with Index-2 DAEs via the Inexact Low-Rank Newton-ADI Method Peter Benner, Matthias Heinkenschloss, Jens Saak, and Heiko K. Weichelt arXiv Preprint arXiv:1804.01410 [math.NA], April 2018. [S11] Extended and Improved Criss-Cross Algorithms for Computing the Spectral Value Set Abscissa and Radius Peter Benner, and Tim Mitchell arXiv Preprint arXiv:1712.10067 [math.OC], December 2017. [S10] Model Reduction of Controlled Fokker-Planck and Liouville-von Neumann Equations Peter Benner, Tobias Breiten, Carsten Hartmann, and Burkhard Schmidt arXiv Preprint arXiv:1706.09882 , July 2017. [S9] A Local Discontinuous Galerkin Method for Dirichlet Boundary Control Problems Peter Benner and Hamdullah Yücel Submitted, May 2017. [S8] Fast Solution of the Poisson-Boltzmann Equation with nonaffine Parametrized Boundary Conditions Using the Reduced Basis Method Peter Benner, Lihong Feng, Cleophas Kweyu, and Matthias Stein arXiv Preprint arXiv:1705.08349, May 2017. [S7] Balanced Truncation Model Order Reduction For Quadratic-Bilinear Control Systems Peter Benner and Pawan Goyal arXiv Preprint arXiv:1705.00160, April 2017. [S6] Solving Optimal Control Problems Governed by Random Navier-Stokes Equations Using Low-Rank Methods Peter Benner, Sergey Dolgov, Akwum Onwunta, and Martin Stoll arXiv Preprint arXiv:1703.06097, March 2017. [S5] Relative Perturbation Theory for Quadratic Eigenvalue Problems Peter Benner, Xin Liang, Suzana Miodragović, and Ninoslav Truhar arXiv Preprint arXiv:1602.03420v2 [math.NA], February 2016. [S4] Balanced Truncation of Linear Time-Invariant Systems over Finite-frequency Ranges Xin Du and Peter Benner arXiv Preprint arXiv:1602.04402v1 [cs.SY], February 2016. [S3] Finite-Frequency Model Order Reduction of Linear Systems via Parameterized Frequency-dependent Balanced Truncation Xin Du and Peter Benner arXiv Preprint arXiv:1602.04408v1 [cs.SY], February 2016. [S2] A Note on a Family of Generalized Procrustes Problems Jens Fankhänel and Peter Benner Submitted September 2015 [S1] Balanced Truncation for Descriptor Systems with Many Terminals Peter Benner and André Schneider MPI Magdeburg Preprint MPIMD/13-17, October 2013.

## Refereed articles in journals

NOTE: The versions of the papers that can be downloaded from this page are often the official journal versions with restricted access. Often, preliminary versions in the form of preprints are available. In any case, we advise you to prefer the published articles as they contain the most recent versions. Electronic reprints of the official versions are available on request.

 [J202] New Gramians for Linear Switched Systems: Reachability, Observability, and Model Reduction Igor Pontes Duff, Sara Grundel, and Peter Benner IEEE Transactions on Automatic Control, accepted 20 July 2019. Preliminary version appeared as arXiv Preprint arXiv:1806.00406, June 2018. [J201] Reduced-Order Modelling of Parametric Systems via Interpolation of Heterogeneous Surrogates Yao Yue, Lihong Feng, and Peter Benner Advanced Modeling and Simulation in Engineering Sciences, accepted 19 July 2019. [J200] Optimal Distributed and Tangential Boundary Control for the Unsteady Stochastic Stokes Equations Christoph Trautwein and Peter Benner ESAIM: Control, Optimisation and Calculus of Variations, accepted 6 July 2019. Preliminary version appeared as arXiv Preprint arXiv:1809.00911v1 [math.OC], September 2018. [J199] Balanced Truncation for a Special Class of Bilinear Descriptor Systems Igor Pontes Duff Pereira, Pawan Goyal, and Peter Benner IEEE Control Systems Letters, Vol. 3, Issue 3, pp. 535-540, 2019. DOI: 10.1109/LCSYS.2019.2911904 [J198] A Bilinear H2 Model Order Reduction Approach to Linear Parameter-Varying Systems Peter Benner, Xingang Cao, and Wil Schilders Advances in Computational Mathematics, published online 18 April 2019. DOI: 10.1007/s10444-019-09695-9 [J197] Computing the Density of States for Optical Spectra of Molecules by Low-Rank and QTT Tensor Approximation Peter Benner, Venera Khoromskaia, Boris N. Khoromskij, and Chao Yang Journal of Computational Physics, published online 23 January 2019. DOI: 10.1016/j.jcp.2019.01.011 Preliminary version appeared as arXiv Preprint arXiv:1801.03852 [math.NA], January 2018. [J196] Periodic Switching Strategies for an Isoperimetric Control Problem with Application to Nonlinear Chemical Reactions Peter Benner, Andreas Seidel-Morgenstern, and Alexander Zuyev Applied Mathematical Modelling, Vol. 69, pp. 287-300, 2019. DOI: 10.1016/j.apm.2018.12.005 Preliminary version appeared as arXiv Preprint arXiv:1811.07421 [math.OC], November 2018. [J195] Interpolatory Model Reduction for Quadratic-Bilinear Systems using Error Estimators Mian Ilyas Ahmad, Peter Benner, and Lihong Feng Engineering Computations, Vol. 36, Issue 1, pp. 25-44, 2019. DOI: 10.1108/EC-04-2018-0162 [J194] Optimal Control Problems Constrained by the Stochastic Navier-Stokes Equations with Multiplicative Lévy Noise Peter Benner and Christoph Trautwein Mathematische Nachrichten, Vol. 292, Issue 7, pp. 1444-1461, 2019. DOI: 10.1002/mana.201700185 [J193] A New Two-Sided Projection Technique for Model Reduction of Quadratic-Bilinear Descriptor Systems Mian Ilyas Ahmad, Peter Benner, and Lihong Feng International Journal of Computer Mathematics, Vol. 96, Issue 10, pp. 1899-1909, 2019. DOI: 10.1080/00207160.2018.1542134 [J192] Adaptive Discontinuous Galerkin Approximation of Optimal Control Problems Governed by Transient Convection-Diffusion Equations Hamdullah Yücel, Martin Stoll, and Peter Benner Electronic Transactions on Numerical Analysis, Vol. 48, pp. 407-434, 2018. DOI: 10.1553/etna_vol48s407 Preliminary version appeared as MPI Magdeburg Preprint MPIMD/15-11, July 2015. [J191] Faster and more Accurate Computation of the H∞-Norm via Optimization Peter Benner and Tim Mitchell SIAM Journal on Scientific Computing, Vol. 40, No. 5, pp. A3609–A3635, 2018. DOI: 10.1137/17M1137966 Preliminary version appeared as arXiv Preprint arXiv:1707.02497, July 2017. [J190] Low-Rank Eigenvector Compression of Posterior Covariance Matrices for Linear Gaussian Inverse Problems Peter Benner, Yue Qiu, and Martin Stoll SIAM/ASA Journal on Uncertainty Quantification, Vol. 6, Issue 2, pp. 965-989, 2018. DOI: 10.1137/17M1121342 Preliminary version appeared as arXiv Preprint arXiv:1703.05638, March 2017. [J189] A Low-Rank Inexact Newton-Krylov Method for Stochastic Eigenvalue Problems Peter Benner, Akwum Onwunta, and Martin Stoll Computational Methods in Applied Mathematics(CMAM), Vol. 19, Issue 1, pp. 5-22, 2019. DOI: 10.1515/cmam-2018-0030 Preliminary version appeared as arXiv Preprint arXiv:1710.09470, October 2017. [J188] Space-time Galerkin POD with Application in Optimal Control of Semi-Linear Parabolic Partial Differential Equations Manuel Baumann, Peter Benner and Jan Heiland SIAM Journal on Scientific Computing, Vol. 40, Issue, 3, pp. A1611-A1641, 2018. DOI: 10.1137/17M1135281 Preliminary version appeared as arXiv Preprint arXiv:1611.04050, November 2016. [J187] Model Reduction of Linear Multi-Agent Systems by Clustering and with H2- and H∞-Error Bounds Hidde-Jan Jongsma, Petar Mlinarić, Sara Grundel, Peter Benner, and Harry L. Trentelman Mathematics of Control, Signals, and Systems, Vol. 30, No. 6, pp. 1-38, 2018. DOI: 10.1007/s00498-018-0212-6 Preliminary version appeared as arXiv Preprint arXiv:1610.02432, October 2016. [J186] Comparison of Model Order Reduction Methods for Optimal Sensor Placement for Thermo-Elastic Models Peter Benner, Roland Herzog, Norman Lang, Ilka Riedel, and Jens Saak Engineering Optimization, Vol, 51, No. 3, pp. 465-483, 2019. DOI: 10.1080/0305215X.2018.1469133 [J185] H2-Quasi-Optimal Model Order Reduction for Quadratic-Bilinear Control Systems Peter Benner, Pawan Goyal, and Serkan Gugercin SIAM Journal on Matrix Analysis and Applications, Vol. 39, Issue 2, pp. 983-1032, 2018. DOI: 10.1137/16M1098280 Preliminary version appeared as arXiv Preprint arXiv:1610.03279v1, October 2016. [J184] A GPU-aware Mixed-precision Solver for Low-rank Algebraic Riccati Equations Peter Benner, Ernesto Dufrechou, Pablo Ezzatti, Alfredo Remón, and Jens Saak Concurrency and Computation: Practice and Experience, Vol. 31, Issue 6, e4462, 2019. DOI: 10.1002/cpe.4462 [J183] On Reduced Input-Output Dynamic Mode Decomposition Peter Benner, Christian Himpe, and Tim Mitchell Advances in Computational Mathematics, Vol. 44, Issue 6, pp. 1751-1768, 2018. DOI: 10.1007/s10444-018-9592-x Preliminary version appeared as arXiv Preprint arXiv:1712.08447 [cs.SY], December 2017. [J182] Some Remarks on the Complex J-Symmetric Eigenproblem Peter Benner, Heike Faßbender, and Chao Yang Linear Algebra and Its Applications, Vol. 544, pp. 407-442, 2018. DOI: 10.1016/j.laa.2018.01.014 Preliminary version appeared as MPI Magdeburg Preprint MPIMD/15-12, July 2015. [J181] Model Reduction by Iterative Error System Approximation Lihong Feng, Athanasios C. Antoulas, and Peter Benner Mathematical and Computer Modelling of Dynamical Systems, Vol. 24, Issue 2, pp. 103-118, 2018. DOI: 10.1080/13873954.2018.1427116 [J180] Range-Separated Tensor Format for Many-Particle Modeling Peter Benner, Venera Khoromskaia, and Boris N. Khoromskij SIAM Journal on Scientific Computing, Vol. 40, Issue 2, pp. A1034–A1062, 2017. DOI: 10.1137/16M1098930 Preliminary version appeared as arXiv Preprint arXiv:1606.09218, June 2016. [J179] L∞-Norm Computation for Large-Scale Descriptor Systems Using Structured Iterative Eigensolvers Peter Benner, Ryan Lowe, and Matthias Voigt Numerical Algebra, Control and Optimization (NACO), Vol. 8, Issue 1, pp. 119-133, 2018. DOI: 10.3934/naco.2018007 [J178] Large-Scale Computation of L∞-Norms by a Greedy Subspace Method Nicat Aliyev, Peter Benner, Emre Mengi, Paul Schwerdtner, and Matthias Voigt SIAM Journal on Matrix Analysis and Applications, Vol. 38, No. 4, pp. 1496–1516, 2017. DOI: 10.1137/16M1086200 Preliminary version appeared as arXiv Preprint arXiv:1705.10086, May 2017. [J177] A Linear Quadratic Control Problem for the Stochastic Heat Equation Driven by Q-Wiener Processes Peter Benner and Christoph Trautwein Journal of Mathematical Analysis and Applications, Vol. 457, No. 1, pp. 776-802, 2018. DOI: 10.1016/j.jmaa.2017.08.052 [J176] Exponential Stability and Stabilization of Extended Linearizations via Continuous Updates of Riccati-Based Feedback Peter Benner and Jan Heiland International Journal of Robust and Nonlinear Control, Vol. 28, No. 4, pp. 1218-1232, 2018. DOI: 10.1002/rnc.3949 Preliminary version appeared as arXiv Preprint arXiv:1607.08441, July 2016. [J175] Singular Perturbation Approximation for Linear Systems with Lévy Noise Peter Benner and Martin Redmann Stochastics and Dynamics, Vol. 18, No.4, 1850033, 2018. DOI: 10.1142/S0219493718500338 Preliminary version appeared as MPI Magdeburg Preprint MPIMD/15-22, December 2015. [J174] RADI: A Low-Rank ADI-type Algorithm for Large Scale Algebraic Riccati Equations Peter Benner, Zvonimir Bujanović, Patrick Kürschner, and Jens Saak Numerische Mathematik, Vol. 138, No. 2, pp. 301-330, 2018. DOI: 10.1007/s00211-017-0907-5 Preliminary version appeared as "A Low-Rank Quadratic ADI Algorithm for Algebraic Riccati Equations", arXiv Preprint arXiv:1510.00040 [math.NA], September 2015. [J173] Optimal Control of a Stefan Problem Fully Coupled with Incompressible Navier-Stokes Equations and Mesh Movement Björn Baran, Peter Benner, Jan Heiland, and Jens Saak Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, Vol. 26, No. 2, pp. 11-40, 2018. DOI: 10.2478/auom-2018-0016 [J172] Computing the Stochastic H∞-Norm by a Newton Iteration Tobias Damm, Peter Benner, and Jan Hauth IEEE Control Systems Letters, Vol. 1, No. 1, pp. 92-97, 2017. DOI: 10.1109/LCSYS.2017.2707409 Preliminary version appeared as arXiv Preprint arXiv:1703.04440, March 2017. [J171] An H2-Type Error Bound for Balancing-Related Model Order Reduction of Linear Systems with Lévy Noise Peter Benner and Martin Redmann Systems & Control Letters, Vol. 105, pp. 1-5, 2017. DOI: 10.1016/j.sysconle.2017.04.004 Preliminary version appeared as MPI Magdeburg Preprint MPIMD/15-20, December 2015. [J170] An Index-aware Parametric Model Order Reduction Method for Parametrized Quadratic Differential-Algebraic Equations Nicodemus Banagaaya, Peter Benner, Lihong Feng, Peter Meuris, and Wim Schoenmaker Applied Mathematics and Computation, Vol. 319, pp. 409-424, 2018. DOI: 10.1016/j.amc.2017.04.024 [J169] Moment-Matching Based Model Reduction for Navier-Stokes Type Quadratic-Bilinear Descriptor Systems Mian Ilyas Ahmad, Peter Benner, Pawan Goyal, and Jan Heiland Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM), Vol. 97, No. 10, pp. 1252–1267, 2017. DOI: 10.1002/zamm.201500262 Preliminary version appeared as MPI Magdeburg Preprint MPIMD/15-18, October 2015. [J168] Adaptive POD-DEIM Basis Construction and its Application to a Nonlinear Population Balance System Lihong Feng, Michael Mangold, and Peter Benner AIChE Journal, Vol 63, No. 9, pp. 3832–3844, 2017. DOI: 10.1002/aic.15749 [J167] Some a Posteriori Error Bounds for Reduced-Order Modelling of (Non-)Parametrized Linear Systems Lihong Feng, Athanasios C. Antoulas, and Peter Benner ESAIM: Mathematical Modelling and Numerical Analysis (M2AN), Vol. 51, No. 6, pp. 2127-2158, 2017. DOI: 10.1051/m2an/2017014 Preliminary version appeared as MPI Magdeburg Preprint MPIMD/15-17, October 2015. [J166] POD-DEIM for Efficient Reduction of a Dynamic 2D Catalytic Reactor Model Peter Benner, Jens Bremer, Lihong Feng, Pawan Goyal, and Kai Sundmacher Computers & Chemical Engineering, Vol. 106, pp. 777-784, 2017. DOI: 10.1016/j.compchemeng.2017.02.032 [J165] Adaptive Symmetric Interior Penalty Galerkin Method for Boundary Control Problems Peter Benner and Hamdullah Yücel SIAM Journal on Numerical Analysis, Vol. 55, No. 2, pp. 1101–1133, 2017. DOI: 10.1137/15M1034507 Preliminary version appeared as MPI Magdeburg Preprint MPIMD/15-13, August 2015. [J164] Structure Preserving Iterative Methods for Periodic Projected Lyapunov Equations and their Application in Model Reduction of Periodic Descriptor Systems Peter Benner and Mohammad-Sahadet Hossain Numerical Algorithms, Vol. 76, Issue 4, pp. 881-904, 2017. DOI: 10.1007/s11075-017-0288-y Preliminary version appeared as MPI Magdeburg Preprint MPIMD/15-08, July 2015. [J163] Fast Iterative Solution of the Bethe-Salpeter Eigenvalue Problem Using Low-Rank and QTT Tensor Approximation Peter Benner, Sergey Dolgov, Venera Khoromskaia, and Boris N. Khoromskij Journal of Computational Physics, Vol. 334, pp. 221–239, 2017. DOI: 10.1016/j.jcp.2016.12.047. Preliminary version appeared as arXiv Preprint arXiv:1602.02646v1 [math.NA], February 2016. [J162] An Isoperimetric Optimal Control Problem for a Non-Isothermal Chemical Reactor with Periodic Inputs Alexander Zuyev, Andreas Seidel-Morgernstern, and Peter Benner Chemical Engineering Science, Vol. 161, pp. 206–214, 2017. DOI: 10.1016/j.ces.2016.12.025. [J161] Extending the Gauss-Huard Method for the Solution of Lyapunov Matrix Equations and Matrix Inversion Peter Benner, Pablo Ezzatti, Enrique S. Quintana-Ortí, and Alfredo Remón Concurrency and Computation: Practice and Experience, Vol. 29, No. 9, pp. e4076 (13pp.), 2017. DOI: 10.1002/cpe.4076. [J160] Krylov Subspace-based Model Reduction for a Class of Bilinear Descriptor Systems Pawan Goyal, Mian Ilyas Ahmad, and Peter Benner Journal of Computational and Applied Mathematics, Vol. 315, pp. 303–318, 2017. DOI: 10.1016/j.cam.2016.11.009. Preliminary version appeared as MPI Magdeburg Preprint MPIMD/15-07, May 2015. [J159] Implicit Volterra Series Interpolation for Model Reduction of Bilinear Systems Mian Ilyas Ahmad, Ulrike Baur, and Peter Benner Journal of Computational and Applied Mathematics, Vol. 316, pp. 15-28, 2017. DOI: 10.1016/j.cam.2016.09.048. Preliminary version appeared as MPI Magdeburg Preprint MPIMD/15-21, December 2015. [J158] Accelerating Optimization and Uncertainty Quantification of Nonlinear SMB Chromatography Using Reduced-Order Models Yongjin Zhang, Lihong Feng, Andreas Seidel-Morgenstern, and Peter Benner Computers & Chemical Engineering, Vol. 96, pp. 237-247, 2017. DOI: 10.1016/j.compchemeng.2016.09.017. [J157] Parametric Modeling and Model Order Reduction for (Electro-)Thermal Analysis of Nanoelectronic Structures Lihong Feng, Yao Yue, Nicodemus Banagaaya, Peter Meuris, Wim Schoenmaker, and Peter Benner Journal of Mathematics in Industry, Vol. 6, Art. 10 (16pp.), 2016. DOI: 10.1186/s13362-016-0030-8. [J156] Multipoint Interpolation of Volterra Series and H2-Model Reduction for a Family of Bilinear Descriptor Systems Peter Benner and Pawan Goyal Systems & Control Letters, Vol. 97, pp. 1-11, 2016. DOI: 10.1016/j.sysconle.2016.08.008. Preliminary version appeared as MPI Magdeburg Preprint MPIMD/15-16, September 2015. [J155] Structure Preserving Model Order Reduction of Large Sparse Second-Order Index-1 Systems and Application to a Mechatronics Model Peter Benner, Jens Saak, and M. Monir Uddin Mathematical and Computer Modelling of Dynamical Systems, Vol. 22, Issue 6, pp. 509-523, 2016. DOI: 10.1080/13873954.2016.1218347. Preliminary version appeared as MPI Magdeburg Preprint MPIMD/14-23, December 2014. [J154] Nanoelectronic COupled Problems Solutions - nanoCOPS: Modelling, Multirate, Model Order Reduction, Uncertainty Quantification, Fast Fault Simulation E. J. W. ter Maten, P. A. Putek, M. Günther, R. Pulch, C. Tischendorf, Ch. Strohm, W. Schoenmaker, P. Meuris, B. De Smedt, P. Benner, L. Feng, N. Banagaaya, Y. Yue et al. Journal of Mathematics in Industry, Vol. 7, Art. 2 (19pp.), 2016. DOI: 10.1186/s13362-016-0025-5. Updated and extended version of OP17. [J153] Krylov Subspace Methods for Model Reduction of Quadratic-Bilinear Systems Mian Ilyas Ahmad, Peter Benner, and Imad M. Jaimoukha IET Control Theory & Applications, Vol. 10, Issue 16, pp. 2010–2018, 2016. DOI: 10.1049/iet-cta.2016.0415. [J152] An Inexact Low-Rank Newton-ADI Method for Large-Scale Algebraic Riccati Equations Peter Benner, Matthias Heinkenschloss, Jens Saak, and Heiko K. Weichelt Applied Numerical Mathematics, Vol. 108, pp. 125-142, June 2016. DOI: 10.1016/j.apnum.2016.05.006. Preliminary version appeared as MPI Magdeburg Preprint MPIMD/15-06, May 2015. [J151] Dual Pairs of Generalized Lyapunov Inequalities and Balanced Truncation of Stochastic Linear Systems Peter Benner, Tobias Damm, and Yolanda Rocio Rodriguez Cruz IEEE Transactions on Automatic Control, Vol. 62, No. 2, pp. 782-791, 2017. DOI: 10.1109/TAC.2016.2572881. [J150] Numerical Solution of the Infinite-Dimensional LQR Problem and the Associated Riccati Differential Equations Peter Benner and Hermann Mena Journal of Numerical Mathematics, Vol. 26, Issue 1, pp. 1-20, 2018. DOI: 10.1515/jnma-2016-1039. Preliminary version appeared as MPI Magdeburg Preprint MPIMD/12-13, August 2012. [J149] Computation of Thermo-Elastic Deformations on Machine Tools - A study of Numerical Methods Andreas Naumann, Norman Lang, Marian Partzsch, Michael Beitelschmidt, Peter Benner, Axel Voigt, and Jörg Wensch Production Engineering Research & Development, Vol. 10, Issue 3, pp. 253-263, 2016. DOI: 10.1007/s11740-016-0674-7. [J148] Trigonometric Spline and Spectral Bounds for the Solution of Linear Time-Periodic Systems Peter Benner, Jonas Denißen, and Ludwig Kohaupt Journal of Applied Mathematics and Computing, Vol. 54, Issue 1, pp. 127–157, 2017. DOI: 10.1007/s12190-016-1001-3. Preliminary version appeared as MPI Magdeburg Preprint MPIMD/16-01, January 2016. [J147] Low-Rank Solvers for Unsteady Stokes-Brinkman Optimal Control Problem with Random Data Peter Benner, Sergey Dolgov, Akwum Onwunta, and Martin Stoll Computer Methods in Applied Mechanics and Engineering, Vol. 304, pp. 26-54, 2016. DOI: 10.1016/j.cma.2016.02.004. Preliminary version appeared as MPI Magdeburg Preprint MPIMD/15-10, July 2015. [J146] Balancing Energy and Performance in Dense Linear System Solvers for Hybrid ARM+GPU Juan Pablo Silva, Ernesto Dufrechou, Pablo Ezzatti, Enrique S. Quintana-Ortí, Alfredo Remón, and Peter Benner CLEI Electronic Journal, Vol. 19, Issue 1, Paper 2, 2016. DOI: 10.19153.19.1.2. [J145] Block-diagonal Preconditioning for Optimal Control Problems Constrained by PDEs with Uncertain Inputs Peter Benner, Akwum Onwunta, and Martin Stoll SIAM Journal on Matrix Analysis and Applications, Vol. 37, No. 2, pp. 491–518, 2016. DOI: 10.1137/15M1018502. Preliminary version appeared as MPI Magdeburg Preprint MPIMD/15-05, April 2015. [J144] A Reduced Basis Approach for Calculation of the Bethe-Salpeter Excitation Energies using Low-Rank Tensor Factorizations Peter Benner, Venera Khoromskaia, and Boris N. Khoromskij Molecular Physics, Vol. 114, Issue 7-8, pp. 1148-1161, 2016. DOI: 10.1080/00268976.2016.1149241. [J143] Frequency-Limited Balanced Truncation with Low-Rank Approximations Peter Benner, Patrick Kürschner, and Jens Saak SIAM Journal on Scientific Computing, Vol. 38, Issue 1, pp. A471–A499, 2016. DOI: 10.1137/15M1030911. Preliminary version appeared as MPI Magdeburg Preprint MPIMD/15-09, July 2015. [J142] Time-dependent Dirichlet Conditions in Finite Element Discretizations Peter Benner and Jan Heiland ScienceOpen Research, available online 3 October 2015. DOI: 10.14293/S2199-1006.1.SOR-MATH.AV2JW3.v1. Preliminary version appeared as MPI Magdeburg Preprint MPIMD/15-03, September 2012. [J141] On the Solution of Large-Scale Algebraic Riccati Equations by Using Low-Dimensional Invariant Subspaces Peter Benner and Zvonimir Bujanović Linear Algebra and Its Applications, Vol. 488, pp. 430-459, 2016. DOI: 10.1016/j.laa.2015.09.027. Preliminary version appeared as MPI Magdeburg Preprint MPIMD/14-15, August 2014. [J140] A Fully Adaptive Scheme for Model Order Reduction Based on Moment-Matching Lihong Feng, Jan G. Korvink, and Peter Benner IEEE Transactions on Components, Packaging, and Manufacturing Technology, Vol. 5, No. 12, pp. 1872-1884, 2015. DOI: 10.1109/TCPMT.2015.2491341. Preliminary version appeared as MPI Magdeburg Preprint MPIMD/12-14, September 2012. [J139] An Efficient Output Error Estimation for Model Order Reduction of Parametrized Evolution Equations Yongjin Zhang, Lihong Feng, and Peter Benner SIAM Journal on Scientific Computing, Vol. 37, No. 6, pp. B910–B936, 2015. DOI: 10.1137/140998603. [J138] Unleashing GPU Acceleration for Symmetric Band Linear Algebra Kernels and Model Reduction Peter Benner, Ernestro Dufrechou, Pablo Ezzatti, Enrique S. Quintana-Ortí, and Alfredo Remón Cluster Computing, Vol. 18, Issue 4, pp. 1351-1362, 2015. DOI: 10.1007/s10586-015-0489-x. [J137] A Discontinous Galerkin Method for Optimal Control Problems Governed by a System of Convection-Diffusion PDEs with Nonlinear Reaction Terms Hamdullah Yücel, Martin Stoll, and Peter Benner Computers and Mathematics with Applications, Vol. 70, Issue 10, pp. 2414-2431, 2015. DOI: 10.1016/j.camwa.2015.09.006. MPI Magdeburg Preprint MPIMD/13-10, July 2013. [J136] Estimating the Inf-Sup Constant in Reduced Basis Methods for Time-Harmonic Maxwell's Equations Martin W. Hess, Sara Grundel, and Peter Benner IEEE Transactions on Microwave Theory and Techniques, Vol. 63, Issue 11, pp. 3549-3557, 2015. DOI: 10.1109/TMTT.2015.2473157. Preliminary version appeared as MPI Magdeburg Preprint MPIMD/14-19, November 2014. [J135] Algorithm 961 - FORTRAN 77 Subroutines for the Solution of Skew-Hamiltonian/Hamiltonian Eigenproblems Peter Benner, Vasile Sima, and Matthias Voigt ACM Transactions on Mathematical Software (TOMS), Vol. 42, Issue 3, no. 24, 2016. DOI: 10.1145/2818313. [J134] Balancing Based Model Reduction for Structured Index-2 Unstable Descriptor Systems with Application to Flow Control Peter Benner, Jens Saak, and M. Monir Uddin Numerical Algebra, Control and Optimization (NACO), Vol. 6, Issue 1, pp. 1-20, 2016. DOI: 10.3934/naco.2016.6.1. Preliminary version appeared as MPI Magdeburg Preprint MPIMD/14-20, November 2014. [J133] Modeling Glyphosate Aerial Spray Drift at the Ecuador-Colombia Border Peter Benner, Hermann Mena, and René Schneider Applied Mathematical Modelling, Vol. 40, No. 1, 373–387. 2016. DOI: 10.1016/j.apm.2015.04.057. Preliminary version appeared as MPI Magdeburg Preprint MPIMD/14-08, April 2014. [J132] Recycling BiCGSTAB with an Application to Parametric Model Order Reduction Kapil Ahuja, Eric de Sturler, Lihong Feng, and Peter Benner SIAM Journal on Scientific Computing, Vol. 37, Issue 5, pp. S429-S446, 2015. DOI: 10.1137/140972433. Preliminary version appeared as MPI Magdeburg Preprint MPIMD/13-21, November 2013. [J131] Model Reduction for Stochastic Systems Peter Benner and Martin Redmann Stochastic Partial Differential Equations: Analysis and Computations, Vol. 3, Issue 3, pp. 291-338, 2015. DOI: 10.1007/s40072-015-0050-1. Preliminary version appeared as MPI Magdeburg Preprint MPIMD/14-03, February 2014. [J130] Accelerating PDE Constrained Optimization by the Reduced Basis Method: Application to Batch Chromatography Yongjin Zhang, Lihong Feng, Suzhou Li, and Peter Benner International Journal for Numerical Methods in Engineering, Vol. 104, Issue 11, pp. 983-1007, 2015. DOI: 10.1002/nme.4950. Preliminary version appeared as MPI Magdeburg Preprint MPIMD/14-09, May 2014. [J129] A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems Peter Benner, Serkan Gugercin, and Karen Willcox SIAM Review, Vol. 57, Issue 4, pp. 483–531, 2015. DOI: 10.1137/130932715. Preliminary version appeared as MPI Magdeburg Preprint MPIMD/13-14, August 2013. [J128] Low-Rank Newton-ADI Methods for Large Nonsymmetric Algebraic Riccati Equations Peter Benner, Patrick Kürschner, and Jens Saak Journal of the Franklin Institute, Vol. 353, Issue 5, pp. 1147-1167, 2016. DOI: 10.1016/j.jfranklin.2015.04.016. Preliminary version appeared as MPI Magdeburg Preprint MPIMD/14-21, November 2014. [J127] Semi-Active Damping Optimization of Vibrational Systems using the Parametric Dominant Pole Algorithm Peter Benner, Patrick Kürschner, Zoran Tomljanović, and Ninoslav Truhar Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM), Vol. 96, Issue 5, pp. 604-619, 2016. DOI: 10.1002/zamm.201400158. MPI Magdeburg Preprint MPIMD/14-12, July 2014. [J126] Towards the Identification of Heat Induction in Chip Removing Processes via an Optimal Control Approach Norman Lang, Jens Saak, Peter Benner, Steffen Ihlenfeldt, Steffen Nestmann, and Klaus Schädlich Production Engineering: Development & Research, Vol. 9, Issue 3, pp. 343-349, 2015. DOI: 10.1007/s11740-015-0608-9. [J125] Low Rank Solution of Unsteady Diffusion Equations with Stochastic Coefficients Peter Benner, Akwum Onwunta, and Martin Stoll SIAM/ASA Journal on Uncertainty Quantification, Vol. 3, No. 1, pp. 622–649, 2015. DOI: 10.1137/130937251. Preliminary version appeared as MPI Magdeburg Preprint MPIMD/13-13, August 2013. [J124] Model Order Reduction for Coupled Problems: Survey Peter Benner and Lihong Feng Applied and Computational Mathematics: An International Journal, Vol. 14, No. 1, pp. 3-22, 2015. Preliminary version appeared as MPI Magdeburg Preprint MPIMD/15-02, February 2015. [J123] Riccati-Based Boundary Feedback Stabilization of Incompressible Navier-Stokes Flow Eberhard Bänsch, Peter Benner, Jens Saak, and Heiko K. Weichelt SIAM Journal on Scientific Computing, Vol. 37, No. 2, pp. A832–A858, 2015. DOI: 10.1137/140980016. [J122] Parametric Model Order Reduction with a Small H2-Error Using Radial Basis Functions Peter Benner, Sara Grundel, Nils Hornung Advances in Computational Mathematics, Vol. 41, Issue 5, pp. 1231-1253, 2015. DOI: 10.1007/s10444-015-9410-7. Preliminary version appeared as MPI Magdeburg Preprint MPIMD/14-01, January 2014. [J121] Nonlinear Model Reduction of a Continuous Fluidized Bed Crystallizer Michael Mangold, Dmytro Khlopov, Stefan Palis, Lihong Feng, Peter Benner, Daniel Binev, and Andreas Seidel-Morgenstern Journal of Computational and Applied Mathematics, Vol. 289, pp. 253-266, 2015. DOI: 10.1016/j.cam.2015.01.028. [J120] Two-Sided Projection Methods for Nonlinear Model Order Reduction Peter Benner and Tobias Breiten SIAM Journal on Scientific Computing, Vol. 37, Issue 2, pp. B239–B260, 2015. DOI: 10.1137/14097255X. Preliminary version appeared as MPI Magdeburg Preprint MPIMD/12-12, June 2012. [J119] Positive Operators and Stable Truncation Peter Benner, Tobias Damm, Martin Redmann, and Yolanda Rocio Rodriguez Cruz Linear Algebra and its Applications, Vol. 498, pp. 74-87, 2016. DOI: 10.1016/j.laa.2014.12.005. Preliminary version appeared as MPI Magdeburg Preprint MPIMD/14-11, July 2014. [J118] Fast and Reliable Noise Estimation for Hyperspectral Subspace Identification Peter Benner, Vedran Novaković, Antonio Plaza, Enrique S. Quintana-Ortí, and Alfredo Remón IEEE Geoscience and Remote Sensing Letters, Vol. 12, Issue 6, pp. 1199-1203, June 2015. DOI: 10.1109/LGRS.2014.2388133. [J117] Uncertainty Quantification for Maxwell's Equations Using Stochastic Collocation and Model Order Reduction Peter Benner and Judith Schneider International Journal for Uncertainty Quantification, Vol. 5, No. 3, pp. 195–208, 2015. DOI: 10.1615/Int.J.UncertaintyQuantification.2015010170. Preliminary version appeared as MPI Magdeburg Preprint MPIMD/13-19, October 2013. [J116] Computing the Eigenvalues of Symmetric H2-Matrices by Slicing the Spectrum Peter Benner, Steffen Börm, Thomas Mach, and Knut Reimer Computing and Visualization in Science, Vol. 16, No. 6, pp. 271-282, published online 4 March 2015. DOI: 10.1007/s00791-015-0238-y. Preliminary version appeared as MPI Magdeburg Preprint MPIMD/14-06, March 2014. [J115] Extending Lyapack for the Solution of Band Lyapunov Equations on Hybrid CPU-GPU Platforms Peter Benner, Ernesto Dufrechou, Pablo Ezzatti, Enrique S. Quintana-Ortí, and Alfredo Remón The Journal of Supercomputing, Vol. 71, No. 2, pp. 740-750, 2015. DOI: 10.1007/s11227-014-1322-7. [J114] Self-Generating and Efficient Shift Parameters in ADI Methods for Large Lyapunov and Sylvester Equations Peter Benner, Patrick Kürschner, and Jens Saak Electronic Transactions on Numerical Analysis, Vol. 43, pp. 142-162, 2014. DOI: 10.17617/2.2071065. Preliminary version appeared as MPI Magdeburg Preprint MPIMD/13-18, October 2013. [J113] Parallel Model Order Reduction of Sparse Electromagnetic/Circuit Models Giovanni De Luca, Giulio Antonini, and Peter Benner ACES Journal, Vol. 30, No. 1, S1-21, January 2015. [J112] Adaptive Discontinuous Galerkin Methods for State Constrained Optimal Control Problems Governed by Convection Diffusion Equations Hamdullah Yücel and Peter Benner Computational Optimization and Applications, Vol. 62, pp. 291-321, 2015. DOI: 10.1007/s10589-014-9691-7. Preliminary version appeared as MPI Magdeburg Preprint MPIMD/13-16, September 2013. [J111] Model Order Reduction for a Family of Linear Systems with Application in Parametric and Uncertain Systems Peter Benner and Sara Grundel Applied Mathematics Letters, Vol. 39, pp. 1-6, 2015. DOI: 10.1016/j.aml.2014.08.002. Preliminary version appeared as MPI Magdeburg Preprint MPIMD/14-05, March 2014. [J110] Rational Interpolation Methods for Symmetric Sylvester Equations Peter Benner and Tobias Breiten Electronic Transactions on Numerical Analysis, Vol. 42, pp. 147-164, 2014. DOI: 10.17617/2.2060858. Preliminary version appeared as MPI Magdeburg Preprint MPIMD/13-23, December 2013. [J109] Model Reduction for Linear Simulated Moving Bed Chromatography Systems Using Krylov-Subspace Methods Suzhou Li, Yao Yue, Lihong Feng, Andreas Seidel-Morgenstern, and Peter Benner AIChE Journal, Vol. 60, No. 11, pp. 3773–3783, 2014. DOI: 10.1002/aic.14561. [J108] Model Order Reduction for Linear and Nonlinear Systems: a System-Theoretic Perspective Peter Benner, Ulrike Baur, and Lihong Feng Archives of Computational Methods in Engineering, Vol. 21, No. 4, pp. 331–358, 2014. DOI: 10.1007/s11831-014-9111-2. Preliminary version appeared as MPI Magdeburg Preprint MPIMD/14-07, March 2014. [J107] Model Order Reduction for Systems with Moving Loads Norman Lang, Jens Saak, and Peter Benner at-Automatisierungstechnik, Vol. 62, No. 7, pp. 512-522, 2014. DOI: 10.1515/auto-2014-1095. [J106] Parametric Model Order Reduction of Thermal Models Using the Bilinear Interpolatory Rational Krylov Algorithm Peter Benner and Angelika Bruns Mathematical and Computer Modelling of Dynamical Systems, Vol. 21, Issue 2, pp. 103-129, 2015. DOI: 10.1080/13873954.2014.924534. The hyperlink to the paper (title link) allows 50 free downloads of the full text. Afterwards, it directs to the paper abstract. [J105] A Reduced Basis Method for Microwave Semiconductor Devices with Geometric Variations Martin W. Hess and Peter Benner COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, Vol. 33, No. 4, pp. 1071-1081, 2014. DOI: 10.1108/COMPEL-12-2012-0377. [J104] A Structured Pseudospectral Method for H∞-Norm Computation of Large-Scale Descriptor Systems Peter Benner and Matthias Voigt Mathematics of Control, Signals, and Systems, Vol. 26, No. 2, pp. 303-338, 2014. DOI: 10.1007/s00498-013-0121-7. Preliminary version appeared as MPI Magdeburg Preprint MPIMD/12-10, May 2012. [J103] Using Surrogate Models for Efficient Optimization of Simulated Moving Bed Chromatography Suzhou Li, Lihong Feng, Peter Benner, and Andreas Seidel-Morgenstern Computers & Chemical Engineering, Vol. 67, pp. 121-132, 2014. DOI: 10.1016/j.compchemeng.2014.03.024. [J102] Numerical Solution of Projected Algebraic Riccati Equations Peter Benner and Tatjana Stykel SIAM Journal on Numerical Analysis, Vol. 52, No. 2, pp. 581-600, 2014. DOI: 10.1137/130923993 Preliminary version appeared as MPI Magdeburg Preprint MPIMD/13-06, May 2013. [J101] Trading off Performance for Energy in Linear Algebra Operations with Applications in Control Theory Peter Benner, Pablo Ezzatti, Enrique S. Quintana-Ortí, and Alfredo Remón CLEI Electronic Journal, Vol. 17, No. 1, Paper 3 (12 pages), 2014. DOI: 10.19153/cleiej.17.1.3 [J100] Computing Real Low-Rank Solutions of Sylvester Equations by the Factored ADI Method Peter Benner and Patrick Kürschner Computers and Mathematics with Applications, Vol. 67, Issue 9, pp. 1656–1672, 2014. DOI: 10.1016/j.camwa.2014.03.004 Preliminary version appeared as MPI Magdeburg Preprint MPIMD/13-05, May 2013. [J99] On Optimality of Approximate Low-Rank Solutions of Large-Scale Matrix Equations Peter Benner and Tobias Breiten Systems & Control Letters Vol. 67, pp. 55-64, 2014. DOI: 10.1016/j.sysconle.2014.02.005 Preliminary version appeared as MPI Magdeburg Preprint MPIMD/11-10, December 2011. [J98] Low-Rank Iterative Methods of Periodic Projected Lyapunov Equations and their Application in Model Reduction of Periodic Descriptor Systems Peter Benner, Mohammad-Sahadet Hossain, and Tatjana Stykel Numerical Algorithms, Vol. 67, No. 3, pp. 669–690, 2014. DOI: 10.1007/s11075-013-9816-6 Preliminary version appeared as Chemnitz Scientific Computing Preprints 11-01, TU Chemnitz, February 2011. [J97] Solving Matrix Equations on Multi-Core and Many-Core Architectures Peter Benner, Pablo Ezzatti, Hermann Mena, Enrique S. Quintana-Ortí, and Alfredo Remón Algorithms, Vol. 6, No. 4, pp. 857-870, 2013. DOI: 10.3390/a6040857 Preliminary version appeared as MPI Magdeburg Preprint MPIMD/11-07, October 2011. [J96] On the Squared Smith Method for Large-Scale Stein Equations Peter Benner, Grece El Khoury, and Miloud Sadkane Numerical Linear Algebra with Applications, Vol. 21, Issue 5, pp. 645-665, 2014. DOI: 10.1002/nla.1918 Preliminary version appeared as MPI Magdeburg Preprint MPIMD/12-15, September 2012. [J95] Fast solution of Cahn-Hilliard Variational Inequalities using Implicit Time Discretization and Finite Elements Jessica Bosch, Martin Stoll, and Peter Benner Journal of Computational Physics, Vol. 262, pp. 38-57, 2014. DOI: 10.1016/j.jcp.2013.12.053 Preliminary version appeared as MPI Magdeburg Preprint MPIMD/13-01, January 2013. [J94] A Factored Variant of the Newton Iteration for the Solution of Algebraic Riccati Equations via the Matrix Sign Function Peter Benner, Pablo Ezzatti, Enrique S. Quintana-Ortí, and Alfredo Remón Numerical Algorithms, Vol. 66, No. 2, pp. 363-377, 2014. DOI: 10.1007/s11075-013-9739-2 [J93] Numerical Solution of Large and Sparse Continuous Time Algebraic Matrix Riccati and Lyapunov Equations: A State of the Art Survey Peter Benner and Jens Saak GAMM Mitteilungen, Vol. 36, No. 1, pp. 32-52, 2013. DOI: 10.1002/gamm.201310003 [J92] Discontinuous Galerkin Finite Element Methods with Shock-Capturing for Nonlinear Convection Dominated Models Hamdullah Yücel, Martin Stoll, and Peter Benner Computers & Chemical Engineering, Vol. 58, pp. 278-287, 2013. DOI: 10.1016/j.compchemeng.2013.07.011 Preliminary version appeared as MPI Magdeburg Preprint MPIMD/13-03, January 2013. [J91] Rosenbrock Methods for Solving Differential Riccati Equations Peter Benner and Hermann Mena IEEE Transactions on Automatic Control, Vol. 58, No. 11, pp. 2950-2956, 2013. DOI: 10.1109/TAC.2013.2258495 Preliminary version appeared as MPI Magdeburg Preprint MPIMD/11-06, October 2011. © IEEE. [J90] A Non-Conforming Composite Quadrilateral Finite Element Pair for Feedback Stabilization of the Stokes Equations Peter Benner, Jens Saak, Friedhelm Schieweck, Piotr Skrzypacz, and Heiko K. Weichelt Journal of Numerical Mathematics, Vol. 22, No. 3, pp. 191-220, 2014. DOI: 10.1515/jnma-2014-0009 Preliminary version appeared as MPI Magdeburg Preprint MPIMD/12-19, October 2012. [J89] Fast Evaluation of Time-Harmonic Maxwell's Equations Using the Reduced Basis Method Peter Benner and Martin W. Hess IEEE Transactions on Microwave Theory and Techniques, Vol. 61, No. 6, pp. 2265-2274, 2013. DOI: 10.1109/TMTT.2013.2258167 Preliminary version appeared as MPI Magdeburg Preprint MPIMD/12-17, October 2012. [J88] An Improved Numerical Method for Balanced Truncation for Symmetric Second-Order Systems Peter Benner, Patrick Kürschner, and Jens Saak Mathematical and Computer Modelling of Dynamical Systems, Vol. 19, No. 6, pp. 593-615, 2013. DOI: 10.1080/13873954.2013.794363. Preliminary version appeared as MPI Magdeburg Preprint MPIMD/12-20, November 2012. [J87] Efficient Solution of Large-Scale Saddle Point Systems Arising in Riccati-Based Boundary Feedback Stabilization of Incompressible Stokes Flow Peter Benner, Jens Saak, Martin Stoll and Heiko K. Weichelt SIAM Journal on Scientific Computing, Vol. 35, No. 5, pp. S150-S170, 2013. DOI: 10.1137/120881312. Preliminary version appeared as Preprint SPP1253-130 of the DFG Priority Programme 1253 Optimization with Partial Differential Equations, June 2012. [J86] The LR Cholesky Algorithm for Symmetric Hierarchical Matrices Peter Benner and Thomas Mach Linear Algebra and its Applications, Vol. 439, No. 4, pp. 1150-1166, 2013. DOI: 10.1016/j.laa.2013.03.001. Preliminary version appeared as MPI Magdeburg Preprint MPIMD/12-05, February 2012. [J85] Spectral Characterization and Enforcement of Negative Imaginariness for Descriptor Systems Peter Benner and Matthias Voigt Linear Algebra and its Applications, Vol. 439, No. 4, pp. 1104-1129, 2013. DOI: 10.1016/j.laa.2012.12.044. Preliminary version appeared as MPI Magdeburg Preprint MPIMD/12-09, April 2012. [J84] Low Rank Methods for a Class of Generalized Lyapunov Equations and Related Issues Peter Benner and Tobias Breiten Numerische Mathematik, Vol. 124, No. 3, pp. 441-470, 2013. DOI: 10.1007/s00211-013-0521-0. Preliminary version appeared as MPI Magdeburg Preprint MPIMD/12-03, February 2012. [J83] Subspace Recycling Accelerates the Parametric Macro‐modeling of MEMS Lihong Feng, Peter Benner, and Jan G. Korvink International Journal for Numerical Methods in Engineering, Vol. 94, No. 1, pp. 84-110, 2013. DOI: 10.1002/nme.4449. Preliminary version appeared as Fast Model Reduction of Parametric Systems using Subspace Recycling MPI Magdeburg Preprint MPIMD/12-08, March 2012. [J82] Model Reduction of an Elastic Crankshaft for Elastic Multibody Simulations Christine Nowakowski, Patrick Kürschner, Peter Eberhard, and Peter Benner Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM), Vol. 93, No. 4, pp. 198-216, 2013. DOI: 10.1002/zamm.201200054. Preliminary version appeared as MPI Magdeburg Preprint MPIMD/12-07, March 2012. [J81] Computation of a Compact State Space Model for an Adaptive Spindle Head Configuration with Piezo Actuators using Balanced Truncation M. Monir Uddin, Jens Saak, Burkhard Kranz, and Peter Benner Production Engineering, Vol. 6, No. 6, pp. 577-586, 2012. DOI: 10.1007/s11740-012-0410-x. [J80] Matrix Inversion on CPU-GPU Platforms with Applications in Control Theory Peter Benner, Pablo Ezzatti, Enrique S. Quintana-Ortí, and Alfredo Remón Concurrency and Computation: Practice and Experience, Vol. 25, No. 8, pp. 1170-1182, 2013. DOI: 10.1002/cpe.2933. Preliminary version appeared as MPI Magdeburg Preprint MPIMD/12-02, February 2012. [J79] Interpolation-Based H2-Model Reduction of Bilinear Control Systems Peter Benner and Tobias Breiten SIAM Journal on Matrix Analysis and Applications, Vol. 33, No. 3, pp. 859-885, 2012. DOI: 10.1137/110836742. Preliminary version appeared as MPI Magdeburg Preprint MPIMD/11-02, June 2011. [J78] HPC en simulación y control a gran escala [in Spanish] Peter Benner, Pablo Ezzatti, Hermann Mena, Enrique S. Quintana-Ortí, and Alfredo Remón Revista ELEMENTOS, Vol. 3, No. 3, pp. 9-35, 2013. [J77] Efficient Handling of Complex Shift Parameters in the Low-Rank Cholesky Factor ADI method Peter Benner, Patrick Kürschner, and Jens Saak Numerical Algorithms, Vol. 62, No. 2, pp. 225-251, 2013. DOI: 10.1007/s11075-012-9569-7. Preliminary version appeared as MPI Magdeburg Preprint MPIMD/11-08, October 2011. [J76] A Mathematical Biography of Danny C. Sorensen Peter Benner, Mark Embree, Richard B. Lehoucq, and C.T. Kelley Linear Algebra and its Applications, Vol. 436, Issue 8, pp. 2717-2724, 2012. DOI: 10.1016/j.laa.2012.01.031. [J75] The Preconditioned Inverse Iteration for Hierarchical Matrices Peter Benner and Thomas Mach Numerical Linear Algebra with Applications, Vol. 20, No. 1, pp. 150-166, 2013. DOI: 10.1002/nla.1830. Preliminary version appeared as MPI Magdeburg Preprint MPIMD/11-01, February 2011. [J74] Optimal Damping of Selected Eigenfrequencies Using Dimension Reduction Peter Benner, Zoran Tomljanović, and Ninoslav Truhar Numerical Linear Algebra with Applications, Vol. 20, No. 1, pp. 1-17, 2013. DOI: 10.1002/nla.833. Preliminary version appeared as Preprint 1/2011, Department of Mathematics, J. J. Strossmayer University of Osijek, March 2011. [J73] Computing All or Some Eigenvalues of Symmetric ℋℓ-Matrices Peter Benner and Thomas Mach SIAM Journal on Scientific Computing, Vol. 34, Issue 1, pp. A485-A496, 2012. DOI: 10.1137/100815323. Preliminary version appeared as MPI Magdeburg Preprint MPIMD/10-01, November 2010. [J72] L∞-Norm Computation for Continuous-Time Descriptor Systems Using Structured Matrix Pencils Peter Benner, Vasile Sima, and Matthias Voigt IEEE Transactions on Automatic Control, Vol. 57, No. 1, pp. 233-238, 2012. DOI: 10.1109/TAC.2011.2161833. [J71] Interpolatory Projection Methods for Parameterized Model Reduction Ulrike Baur, Christopher Beattie, Peter Benner, and Serkan Gugercin SIAM Journal on Scientific Computing, Vol. 33, Issue 5, pp. 2489-2518, 2011. DOI: 10.1137/090776925. Preliminary version appeared as Chemnitz Scientific Computing Preprints 09-08, TU Chemnitz, November 2009. [J70] Generalized Tangential Interpolation for Model Reduction of Discrete-Time MIMO Bilinear Systems Peter Benner, Tobias Breiten, and Tobias Damm International Journal of Control, Vol. 84, No. 8 pp. 1398-1407, 2011. DOI: 10.1080/00207179.2011.601761. Preliminary version appeared as MPI Magdeburg Preprint MPIMD/10-02, December 2010. [J69] Robust Formulas for Optimal H∞ Controllers Peter Benner, Ralph Byers, Philip Losse, Volker Mehrmann, and Hongguo Xu Automatica, Vol. 47, No. 12, pp. 2639-2646, 2011. DOI: 10.1016/j.automatica.2011.09.013. Preliminary version appeared as Preprint 20-2010, Preprint series of the Institute of Mathematics, Technische Universität Berlin, September 2010. [J68] Lyapunov Equations, Energy Functionals, and Model Order Reduction of Bilinear and Stochastic Systems Peter Benner and Tobias Damm SIAM Journal on Control and Optimization, Vol. 49, No. 2, pp. 686-711, 2011. DOI: 10.1137/09075041X. [J67] A Mixed-Precision Algorithm for the Solution of Lyapunov Equations on Hybrid CPU-GPU Platforms Peter Benner, Pablo Ezzatti, Daniel Kressner, Enrique S. Quintana-Ortí, and Alfredo Remón Parallel Computing, Vol. 37, Issue 8, pp. 439–450, 2011. DOI: 10.1016/j.parco.2010.12.002. Preliminary version appeared as Research Report No. 2009-40, Seminar für Angewandte Mathematik, ETH Zürich, December 2009. [J66] Efficient Balancing-Based MOR for Large-Scale Second-Order Systems Peter Benner and Jens Saak Mathematical and Computer Modelling of Dynamical Systems, Vol. 17, No. 2, pp. 123-143, 2011. Author Posting. (c) Taylor & Francis, 2011. This is the author's version of the work. It is posted here by permission of Taylor & Francis for personal use, not for redistribution. The definitive version was published in January 2011. DOI: 10.1080/13873954.2010.540822. [J65] Dimension Reduction for Damping Optimization in Linear Vibrating Systems Peter Benner, Zoran Tomljanović, and Ninoslav Truhar Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM), Vol. 91, No. 3, pp. 179–191, 2011. Editor's choice of this ZAMM issue! DOI: 10.1002/zamm.201000077. Preliminary version appeared as Preprint 2/2010, Department of Mathematics, J. J. Strossmayer University of Osijek, April 2010. [J64] On the Numerical Solution of Large-Scale Sparse Discrete-Time Riccati Equations Peter Benner and Heike Faßbender Advances in Computational Mathematics, Vol. 35, No. 2-4, pp. 119-147, 2011. DOI: 10.1007/s10444-011-9174-7. Preliminary version appeared as Chemnitz Scientific Computing Preprints 09-11, TU Chemnitz, December 2009. [J63] Parameter Preserving Model Order Reduction for MEMS Applications Ulrike Baur, Peter Benner, Andreas Greiner, Jan G. Korvink, Jan Lienemann, and Christian Moosmann Mathematical and Computer Modelling of Dynamical Systems, Vol. 17, No. 4, pp. 297-317, 2011. DOI: 10.1080/13873954.2011.547658. [J62] A Hamiltonian Krylov-Schur-type method based on the symplectic Lanczos process Peter Benner, Heike Faßbender, and Martin Stoll Linear Algebra and its Applications, Vol. 435, Issue 3, pp. 578-600, 2011. DOI: 10.1016/j.laa.2010.04.048. Preliminary version appeared as OCCAM Report Number 09/32, Oxford Centre for Collaborative Applied Mathematics, July 2009. [J61] On the QR Decomposition of H-Matrices. Peter Benner and Thomas Mach Computing, Vol. 88, No. 3-4, pp. 111-129, 2010. DOI: 10.1007/s00607-010-0087-y. See also Chemnitz Scientific Computing Preprints09-04, TU Chemnitz, July 2009. [J60] Die SLICOT-Toolboxen für Matlab (The SLICOT-Toolboxes for Matlab) [German] Peter Benner, Daniel Kressner, Vasile Sima, and Andras Varga at-Automatisierungstechnik, Vol. 58, Issue 1, pp. 15-25, 2010. DOI: 10.1524/auto.2010.0814. For an English version, see The SLICOT Toolboxes - a Survey, SLICOT Working Note 2009-1, August 2009. [J59] Modale versus moderne Ordnungsreduktionsverfahren: Effiziente Simulation von Werkzeugmaschinen [German] Thomas Bonin, Michael Zäh, Andreas Soppa, Heike Faßbender, Jens Saak, and Peter Benner MECHATRONIK, Vol. 11-12/2009, pp. 46-47, 2009. [J58] On the ADI Method for Sylvester Equations Peter Benner, Reng-Cang Li, and Ninoslav Truhar Journal of Computational and Applied Mathematics, Vol. 233, No. 4, pp. 1035-1045, 2009. DOI: 10.1016/j.cam.2009.08.108. [J57] Model Reduction for Parametric Systems Using Balanced Truncation and Interpolation [German] Ulrike Baur and Peter Benner at-Automatisierungstechnik Vol. 57, No. 8, pp. 411-419, 2009. DOI: 10.1524/auto.2009.0787. [J56] A Rational SHIRA Method for the Hamiltonian Eigenvalue Problem Peter Benner and Cedric Effenberger Taiwanese Journal of Mathematics, Vol. 14, No. 3A, pp. 805-823, 2010. See also Chemnitz Scientific Computing Preprints 08-08, TU Chemnitz, December 2008. [J55] 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. See also Numerical Analysis Group Research Report NA-07/03, Oxford University, February 2007. [J54] Cross-Gramian Based Model Reduction for Data-Sparse Systems Ulrike Baur and Peter Benner Electronic Transactions on Numerical Analysis, Vol. 31, pp. 256-270, 2008. [J53] Numerical Solution of Large Lyapunov Equations, Riccati Equations, and Linear-Quadratic Control Problems Peter Benner, Jing-Rebecca Li, and Thilo Penzl Numerical Linear Algebra with Applications, Vol. 15, No. 9, pp. 755-777, 2008. DOI: 10.1002/nla.622 [J52] Gramian-Based Model Reduction for Data-Sparse Systems Ulrike Baur and Peter Benner SIAM Journal on Scientific Computing, Vol. 31, No. 1, pp. 776-798, 2008. DOI: 10.1137/070711578 See also Chemnitz Scientific Computing Preprints 07-01, TU Chemnitz, February 2007. [J51] Solving Linear-Quadratic Optimal Control Problems on Parallel Computers Peter Benner, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí Optimization Methods and Software, Vol. 23, No. 6, pp. 879-909, 2008. DOI: 10.1080/10556780802058721 See also: Preprint SFB393/05-19, Sonderforschungsbereich 393 - Numerische Simulation auf massiv parallelen Rechnern, TU Chemnitz, March 2006. [J50] On the Parameter Selection Problem in the Newton-ADI Iteration for Large-Scale Riccati Equations Peter Benner, Hermann Mena, and Jens Saak Electronic Transactions on Numerical Analysis, Vol. 29, pp. 136-149, 2008. [J49] Efficient Algorithms for Generalized Algebraic Bernoulli Equations based on the Matrix Sign Function Sergio Barrachina, Peter Benner, and Enrique S. Quintana-Ortí Numerical Algorithms, Vol. 46, No. 4, pp. 351-368, 2007. DOI: 10.1007/s11075-007-9143-x Partially extracted from [TR15]. [J48] A Robust Numerical Method for the $\gamma$-Iteration in $H_\infty$ Control Peter Benner, Ralph Byers, Volker Mehrmann, and Hongguo Xu Linear Algebra and its Applications, Vol. 425, No. 2-3, pp. 548-570, 2007. DOI: 10.1016/j.laa.2007.03.026 Revised version of [TR13]. [J47] On the Solution of the Rational Matrix Equation X = Q + LX^{-1}L^T Peter Benner and Heike Faßbender EURASIP Journal on Advances in Signal Processing, special issue on "Numerical Linear Algebra in Signal Processing Application", Vol. 2007, Article ID 21850, 10 pages, 2007. DOI: 10.1155/2007/21850 See also: Chemnitz Scientific Computing Preprints 06-02, TU Chemnitz, September 2006. [J46] Factorized Solution of Lyapunov Equations Based on Hierarchical Matrix Arithmetic Ulrike Baur and Peter Benner Computing, Vol. 78, No. 3, pp. 211-234, 2006. DOI: 10.1007/s00607-006-0178-y [J45] Stabilizing Large-Scale Generalized Systems on Parallel Computers Using Multithreading and Message-Passing Peter Benner, Maribel Castillo, Rafael Mayo, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí Concurrency and Computation: Practice and Experience, Vol. 19, No. 4, pp. 531-542, 2007. DOI: 10.1002/cpe.1148 [J44] Partial Realization of Descriptor Systems Peter Benner and Viatcheslav I. Sokolov Systems & Control Letters, Vol. 55, Issue 11, pp. 929-938, 2006. DOI: 10.1016/j.sysconle.2006.06.009 [J43] Evaluation of the Linear Matrix Equation Solvers in SLICOT Martin Slowik, Peter Benner, and Vasile Sima Journal of Numerical Analysis, Industrial and Applied Mathematics, Vol. 2, No. 1-2, pp. 11-34, 2007. Extendend version appeared as SLICOT Working Note 2004-1, August 2004. [J42] An Arithmetic for Matrix Pencils: Theory and New Algorithms Peter Benner and Ralph Byers Numerische Mathematik, Vol. 103, No. 4, pp. 539-573, 2006. DOI: 10.1007/s00211-006-0001-x [J41] Numerische Methoden zur passivitätserhaltenden Modellreduktion (Numerical Methods for Passivity Preserving Model Reduction) (in German) Peter Benner and Heike Faßbender at-Automatisierungstechnik, Vol. 54, No. 4, pp. 153-160, 2006. DOI: 10.1524/auto.2006.54.4.153 [J40] Numerical Linear Algebra for Model Reduction in Control and Simulation Peter Benner GAMM Mitteilungen, Vol. 29, No. 2, pp. 275-296, 2006. DOI: 10.1002/gamm.201490034 See also Preprint 18/2005, Fakultät für Mathematik, TU Chemnitz. [J39] Parallel Solution of Large-Scale Algebraic Bernoulli Equations with the Matrix Sign Function Method Sergio Barrachina, Peter Benner, and Enrique S. Quintana-Ortí International Journal of Computational Science and Engineering, Vol. 4, No. 2, pp. 88-93, 2009. DOI: 10.1504/IJCSE.2009.027000 Extended version of [CA45]. [J38] Algorithm 854: Fortran 77 Subroutines for Computing the Eigenvalues of Hamiltonian Matrices Peter Benner and Daniel Kressner ACM Transactions on Mathematical Software, Vol. 32, No. 2, pp. 352-373, 2006. DOI: 10.1145/1141885.1141895 For the corresponding software visit the HAPACK homepage. [J37] Solving Stable Sylvester Equations via Rational Iterative Schemes Peter Benner, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí Journal of Scientific Computing, Vol. 28, No. 1, pp. 51-83, 2006. DOI: 10.1007/s10915-005-9007-2 Note: in Algorithm 3, Step 9 must read: U := U-CB; in Example 1, the entries of the solution matrix X need to be negated. [J36] Balancing Sparse Hamiltonian Eigenproblems Peter Benner and Daniel Kressner Linear Algebra and its Applications, Vol. 415, Issue 1, pp. 3-19, 2006. Original available from ScienceDirect, DOI: 10.1016/j.laa.2004.09.023 [J35] Partial Stabilization of Large-Scale Discrete-Time Linear Control Systems Peter Benner, Maribel Castillo, and Enrique S. Quintana-Ortí International Journal of Computational Science and Engineering, Vol. 1, No. 1, pp. 15-21, 2005. DOI: 10.1504/IJCSE.2005.008907 See also [CA19] [J34] Solving Large-Scale Control Problems Peter Benner IEEE Control Systems Magazine, Vol. 24, No. 1, pp. 44-59, 2004. DOI: 10.1109/MCS.2004.1272745 [J33] Parallel Algorithms for Model Reduction of Discrete-Time Systems Peter Benner, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí International Journal of System Sciences, Vol. 34, No. 5, pp. 319-333, 2003. DOI: 10.1080/0020772031000158564 The retrievable version appeared as Berichte aus der Technomathematik, Report 00-18, December 2000. [J32] State-Space Truncation Methods for Parallel Model Reduction of Large-Scale Systems Peter Benner, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí Parallel Computing, Vol. 29 (special issue on "Parallel and Distributed Scientific and Engineering Computing"), Issue 11-12, pp. 1701-1722, 2003. DOI: 10.1016/j.parco.2003.05.013 [J31] Structure Preservation: A Challenge in Computational Control Peter Benner, Daniel Kressner, and Volker Mehrmann Future Generation Computer Systems, Vol. 19, Issue 7, pp. 1243-1252, 2003. DOI: 10.1016/S0167-739X(03)00049-9 [J30] The Kleinman Iteration for Nonstabilizable Systems Peter Benner, Vicente Hernández, and Antonio Pastor Mathematics of Control, Signals, and Systems , Vol. 16, Issue 1,pp. 76-93, 2003. DOI: 10.1007/s00498-003-0130-z The retrievable version appeared as Berichte aus der Technomathematik, Report 99-11, October 1999. [J29] Numerical Solution of Discrete Stable Linear Matrix Equations on Multicomputers Peter Benner, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí Parallel Algorithms and Applications (since 2005: International Journal of Parallel, Emergent and Distributed Systems) Vol. 17, No. 2, pp. 127-146, 2002. DOI: 10.1080/10637190208941436 Free preprint available at Berichte aus der Technomathematik, Report 99-13, November 1999. [J28] Numerical Computation of Deflating Subspaces of Skew-Hamiltonian/Hamiltonian Pencils Peter Benner, Ralph Byers, Volker Mehrmann, and Hongguo Xu SIAM Journal on Matrix Analysis and Applications, Vol. 24, No. 1, pp. 165-190, 2002. DOI: 10.1137/S0895479800367439 For an extended version, including detailed algorithms, see [TR10] . [J27] Parallel Algorithms for LQ Optimal Control of Discrete-Time Periodic Linear Systems Peter Benner, Ralph Byers, Rafael Mayo, Enrique S. Quintana-Ortí, and Vicente Hernández Journal of Parallel and Distributed Computing, Vol. 62, Issue 2, pp. 306-325, 2002. DOI: 10.1006/jpdc.2001.1790 The retrievable version appeared as Berichte aus der Technomathematik, Report 01-02, February 2001. [J26] Efficient Numerical Algorithms for Balanced Stochastic Truncation Peter Benner, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí International Journal of Applied Mathematics and Computer Science, Vol. 11, No. 5, pp. 1123-1150, 2001. The retrievable version appeared as Berichte aus der Technomathematik, Report 01-03, March 2001. [J25] Perturbation Analysis for the Eigenvalue Problem of a Formal Product of Matrices Peter Benner, Volker Mehrmann, and Hongguo Xu BIT, Vol. 42, No. 1, pp. 1-43, 2002. DOI: 10.1023/A:1021966001542 The retrievable version appeared as Berichte aus der Technomathematik, Report 00-01, January 2000. [J24] A Hybrid Method for the Numerical Solution of Discrete-Time Algebraic Riccati Equations Peter Benner and Heike Faßbender Contemporary Mathematics, Vol. 280, pp. 255-269, 2001. The retrievable version appeared as Berichte aus der Technomathematik, Report 99-12, October 1999. [J23] Cholesky-like Factorizations of Skew-Symmetric Matrices Peter Benner, Ralph Byers, Heike Faßbender, Volker Mehrmann, and David S. Watkins Electronic Transactions on Numerical Analysis, Vol. 11, pp. 85-93, 2000. [J22] Symplectic Balancing of Hamiltonian Matrices Peter Benner SIAM Journal on Scientific Computing, Vol. 22, No. 5, pp. 1885-1904, 2001. DOI: 10.1137/S1064827500367993 [J21] Evaluating Products of Matrix Pencils and Collapsing Matrix Products Peter Benner and Ralph Byers Numerical Linear Algebra with Applications, Vol. 8, No. 6-7, pp. 357-380, 2001. DOI: 10.1002/nla.251 [J20] Balanced Truncation Model Reduction of Large-Scale Dense Systems on Parallel Computers Peter Benner, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí Mathematical and Computer Modelling of Dynamical Systems, Vol. 6, No.4, pp. 383-405, 2000. DOI: 10.1076/mcmd.6.4.383.3658 The retrievable version appeared as Berichte aus der Technomathematik, Report 99-07, September 1999. [J19] An Implicitly Restarted Symplectic Lanczos Method for the Symplectic Eigenvalue Problem Peter Benner and Heike Faßbender SIAM Journal on Matrix Analysis and Applications, Vol. 22, No. 3, pp. 682-713, 2001. DOI: 10.1137/S0895479898343115 Retrieve preprint: Berichte aus der Technomathematik, Report 98-01, July 1998. [J18] Algorithm 800: Fortran 77 Subroutines for Computing the Eigenvalues of Hamiltonian Matrices I: The Square-Reduced Method Peter Benner, Ralph Byers, and Eric Barth ACM Transactions on Mathematical Software, Vol. 26, No. 1, pp. 49-77, 2000. DOI: 10.1145/347837.347852 For the corresponding software, click here (shell script, compressed using gzip). See also: [TR5] and Peter Benner's software. [J17] Solving Algebraic Riccati Equations on Parallel Computers Using Newton's Method with Exact Line Search Peter Benner, Ralph Byers, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí Parallel Computing, Vol. 26, No. 10, pp. 1345-1368, 2000. DOI: 10.1016/S0167-8191(00)00012-0 The retrievable version appeared as Berichte aus der Technomathematik, Report 98-05, August 1998. [J16] A Note on the Numerical Solution of Complex Hamiltonian and Skew-Hamiltonian Eigenvalue Problems Peter Benner, Volker Mehrmann, and Hongguo Xu Electronic Transactions on Numerical Analysis, Vol. 8, pp. 115-126, 1999. [J15] Solving Stable Generalized Lyapunov Equations with the Matrix Sign Function Peter Benner and Enrique S. Quintana-Ortí Numerical Algorithms, Vol. 20, No. 1, pp. 75-100, 1999. DOI: 10.1023/A:1019191431273 Preliminary version appeared as Preprint SFB393/97-23, Sonderforschungsbereich 393 - Numerische Simulation auf massiv parallelen Rechnern, TU Chemnitz, October 1997. [J14] Parallel Partial Stabilizing Algorithms for Large Linear Control Systems Peter Benner, Maribel Castillo, Enrique S. Quintana-Ortí, and Vicente Hernández The Journal of Supercomputing, Vol. 15, Issue 2, pp. 193-206, 2000. DOI: 10.1023/A:1008108004247 The retrievable version appeared as Berichte aus der Technomathematik, Report 98-03, July 1998. [J13] Parallel Distributed Solvers for Large Stable Generalized Lyapunov Equations Peter Benner, José M. Claver, and Enrique S. Quintana-Ortí DOI: 10.1142/S0129626499000165 Parallel Processing Letters, Vol. 9, No. 1, pp. 147-158, 1999. [J12] SR and SZ Algorithms for the Symplectic (Butterfly) Eigenproblem Peter Benner, Heike Faßbender, and David S. Watkins Linear Algebra and its Applications, Vol. 287, Issue 1-3, pp. 41-76, 1999. DOI: 10.1016/S0024-3795(98)10090-3 [J11] SLICOT - A Subroutine Library in Systems and Control Theory Peter Benner, Volker Mehrmann, Vasile Sima, Sabine Van Huffel, and Andras Varga Applied and Computational Control, Signals, and Circuits, Vol. 1, pp. 505-546, 1999. The retrievable version appeared as NICONET Report 97-03, Working Group on Software, June 1997. [J10] Computational Methods for Linear-Quadratic Optimization Peter Benner Rendiconti del Circolo Matematico di Palermo, Supplemento, Serie II, No. 58, pp. 21-56, 1999. Extendend version appeared as Berichte aus der Technomathematik, Report 98-04, August 1998. [J9] The Symplectic Eigenvalue Problem, the Butterfly Form, the SR Algorithm, and the Lanczos Method Peter Benner and Heike Faßbender Linear Algebra and its Applications, Vol. 275/276, pp. 19-47, 1998. DOI: 10.1016/S0024-3795(97)10049-0 [J8] A Numerically Stable, Structure Preserving Method for Computing the Eigenvalues of Real Hamiltonian or Symplectic Pencils Peter Benner, Volker Mehrmann, and Hongguo Xu Numerische Mathematik, Vol. 78, No. 3, pp. 329-358, 1998. DOI: 10.1007/s002110050315 [J7] An Exact Line Search Method for Solving Generalized Continuous-Time Algebraic Riccati Equations Peter Benner and Ralph Byers IEEE Transactions on Automatic Control, Vol. 43, No. 1, pp. 101-107, 1998. See also: [TR3] . [J6] Two Connections between the SR and HR Eigenvalue Algorithms Peter Benner, Heike Faßbender, and David S. Watkins Linear Algebra and its Applications, Vol. 272, Issue 1-3, pp. 17-32, 1998. DOI: 10.1016/S0024-3795(97)00279-6 [J5] A New Method for Computing the Stable Invariant Subspace of a Real Hamiltonian Matrix Peter Benner, Volker Mehrmann and Hongguo Xu Journal of Computational and Applied Mathematics, Vol. 86, Issue 1, pp. 17-43, 1997. DOI: 10.1016/S0377-0427(97)00146-5 [J4] NICONET, a Network for Numerically Reliable Software in CACSD Ad J.W. van den Boom, Sabine Van Huffel, and Peter Benner Journal A - Benelux Quarterly Journal on Automatic Control, Vol. 38, No. 3, pp. 20-21, 1997. [J3] Benchmarks for the Numerical Solution of Algebraic Riccati Equations Peter Benner, Alan J. Laub, and Volker Mehrmann IEEE Control Systems Magazine, Vol. 17, No. 5, pp. 18-28, 1997. DOI: 10.1109/37.621466 See also: [TR1], [TR2] [J2] 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. DOI: 10.1016/S0024-3795(96)00524-1 See also: [TR4] [J1] A Multishift Algorithm for the Numerical Solution of Algebraic Riccati Equations Gregory Ammar, Peter Benner, and Volker Mehrmann Electronic Transactions on Numerical Analysis, Vol. 1, pp. 33-48, 1993.

## Book chapters

 [BC35] Gas Network Benchmark Models Peter Benner, Sara Grundel, Christian Himpe, Christoph Huck, Tom Streubel, and Caren Tischendorf In S. Campbell, A. Ilchmann, V. Mehrmann, T. Reis (Eds.), Applications of Differential-Algebraic Equations: Examples and Benchmarks, pp. 171-197, 2019. DOI: 10.1007/11221_2018_5 [BC34] GPU Accelerated and Storage-Efficient Implementation of the QR Decomposition Peter Benner, Martin Köhler, and Carolin Penke In S. Bassini, M. Danelutto, P. Dazzi, G. R. Joubert, F. Peters (Eds.), Parallel Computing is Everywhere, Vol. 32, pp. 329-338, 2018 DOI: 10.3233/978-1-61499-843-3-329 [BC33] A Direct Index 1 DAE Model of Gas Networks Peter Benner, Maike Braukmüller, and Sara Grundel In W. Keiper, A. Milde, S. Volkwein (Eds.), Reduced-Order Modeling (ROM) for Simulation and Optimization, pp. 99-119, Springer, Cham, 2018. DOI: 10.1007/978-3-319-75319-5_5 [BC32] An Iterative Model Reduction Scheme for Quadratic-Bilinear Descriptor Systems with an Application to Navier-Stokes Equations Peter Benner and Pawan Goyal In W. Keiper, A. Milde, S. Volkwein (Eds.), Reduced-Order Modeling (ROM) for Simulation and Optimization, pp. 1-19, Springer, Cham, 2018. DOI: 10.1007/978-3-319-75319-5_1 Preliminary version appeared as arXiv Preprint arXiv:1705.00934, April 2017. [BC31] Reduced Representation of Power Grid Models Peter Benner and André Schneider In P. Benner (Ed.), System Reduction for Nanoscale IC Design, Mathematics in Industry, Vol. 20, pp. 87-134, Springer International Publishing, Cham, 2017. DOI: 10.1007/978-3-319-07236-4_3 [BC30] Comparison of Methods for Parametric Model Order Reduction of Time-Dependent Problems Ulrike Baur, Peter Benner, Bernard Haasdonk, Christian Himpe, Immanuel Maier, and Mario Ohlberger In P. Benner, A. Cohen, M. Ohlberger, K. Willcox (Eds.), Model Reduction and Approximation: Theory and Algorithms, Chapter 9, pp. 377-407, SIAM Publications, Philadelphia, PA, 2017. DOI: 10.1137/1.9781611974829.ch9 Preliminary version appeared as MPI Magdeburg Preprint MPIMD/15-01, February 2015. [BC29] Model Order Reduction Based on System Balancing Peter Benner and Tobias Breiten In P. Benner, A. Cohen, M. Ohlberger, K. Willcox (Eds.), Model Reduction and Approximation: Theory and Algorithms, Chapter 6, pp. 261-295, SIAM Publications, Philadelphia, PA, 2017. DOI: 10.1137/1.9781611974829 [BC28] Truncated Gramians for Bilinear Systems and their Advantages in Model Order Reduction Peter Benner, Pawan Goyal, and Martin Redmann In P. Benner, M. Ohlberger, T. Patera, G. Rozza, K. Urban (Eds.), Model Reduction of Parametrized Systems, MS&A - Modeling, Simulation and Applications, Springer International Publishing, Cham, Vol. 17, pp. 285-300, 2017. DOI: 10.1007/978-3-319-58786-8_18 [BC27] Reduced Basis Approximations for Maxwell’s Equations in Dispersive Media Peter Benner and Martin W. Hess In P. Benner, M. Ohlberger, T. Patera, G. Rozza, K. Urban (Eds.), Model Reduction of Parametrized Systems, MS&A - Modeling, Simulation and Applications, Springer International Publishing, Cham, Vol. 17, pp. 107-119, 2017. DOI: 10.1007/978-3-319-58786-8_7 [BC26] Model Order Reduction for Differential-Algebraic Equations: a Survey Peter Benner and Tatjana Stykel In A. Ilchmann, T. Reis (Eds.), Surveys in Differential-Algebraic Equations IV, Differential-Algebraic Equations Forum, Springer International Publishing, pp. 107-160, 2017. DOI: 10.1007/978-3-319-46618-7_3 A preliminary version is available as MPI Magdeburg Preprint MPIMD/15-19, November 2015. [BC25] Theory and Numerical Solution of Differential and Algebraic Riccati Equations Peter Benner In P. Benner, M. Bollhöfer, D. Kressner, Ch. Mehl, and T. Stykel (Eds.), Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory, Part I, pp. 67-105, Springer International Publishing, 2015. DOI: 10.1007/978-3-319-15260-8_4 [BC24] Numerical Linear Algebra Methods for Linear Differential-Algebraic Equations Peter Benner, Philip Losse, Volker Mehrmann, and Matthias Voigt In A. Ilchmann, T. Reis (Eds.), Surveys in Differential-Algebraic Equations III, pp. 117-175, Differential-Algebraic Equations Forum, Springer International Publishing, 2015. DOI: 10.1007/978-3-319-22428-2_3 A preliminary version with slightly different focus is available as Preprint [TR26] [BC23] Matrix Equations and Model Reduction Peter Benner, Tobias Breiten, and Lihong Feng In Z. Bai, W. Gao, and Y. Su (Eds.), Matrix Functions and Matrix Equations, Series in Contemporary Applied Mathematics, Chapter 3, pp. 50-75, World Scientific, 2015. DOI: 10.1142/9789814675772_0003 [BC22] Model Order Reduction for Thermo-Elastic Assembly Group Models Peter Benner, Norman Lang, and Jens Saak In K. Großmann (Eds.), Thermo-energetic Design of Machine Tools, Lecture Notes in Production Engineering, Chapter 8/pp.85-93, Springer International Publishing, 2015. [ISBN: 978-3-319-12624-1] DOI: 10.1007/978-3-319-12625-8_8 [BC21] LQG-Balanced Truncation Low-Order Controller for Stabilization of Laminar Flows Peter Benner and Jan Heiland In R. King (Ed.), Active Flow and Combustion Control 2014, Notes on Numerical Fluid Mechanics and Multidisciplinary Design, Vol. 127, pp. 365-379, Springer International Publishing, 2015. [ISBN: 978-3-319-11966-3] DOI: 10.1007/978-3-319-11967-0_22 Preliminary version appeared as MPI Magdeburg Preprint MPIMD/14-04, March 2014. [BC20] Model Order Reduction of Differential Algebraic Equations Arising from the Simulation of Gas Transport Networks Sara Grundel, Lennart Jansen, Nils Hornung, Tanja Clees, Caren Tischendorf, and Peter Benner In S. Schöps, A. Bartel, M. Günther, E. J. W. ter Maten, and P. C. Müller (Eds.), Progress in Differential-Algebraic Equations, Differential-Algebraic Equations Forum, pp. 183-205, Springer-Verlag, Berlin/Heidelberg, 2014. [ISBN: 978-3-662-44925-7] DOI: 10.1007/978-3-662-44926-4_9 Preliminary version appeared as MPI Magdeburg Preprint MPIMD/13-09, June 2013. [BC19] Model Order Reduction: Techniques and Tools Peter Benner and Heike Faßbender In J. Baillieul and T. Samad (Eds.), Encyclopedia of Systems and Control, Springer-Verlag, pp. 722-729, 2015. [ISBN: 978-1-4471-5057-2] DOI: 10.1007/978-1-4471-5058-9_142 [BC18] Model Reduction Peter Benner In N. J. Higham et al. (Eds.), Princeton Companion to Applied Mathematics, Princeton University Press, Princeton, NJ., Part II-26, pp. 117-119, 2015. [BC17] Model Order Reduction for PDE Constrained Optimization Peter Benner, Ekkehard Sachs, and Stefan Volkwein In G. Leugering, P. Benner, S. Engell, A. Griewank, H. Harbrecht, M. Hinze, R. Rannacher, and S. Ulbrich (Eds.), Trends in PDE Constrained Optimization, International Series of Numerical Mathematics, Vol. 165, pp. 303-326, Birkhäuser, Basel, 2014. [ISBN: 978-3-319-05082-9] DOI: 10.1007/978-3-319-05083-6_19 [BC16] Optimal Control-Based Feedback Stabilization of Multi-Field Flow Problems Eberhard Bänsch, Peter Benner, Jens Saak, and Heiko K. Weichelt In G. Leugering, P. Benner, S. Engell, A. Griewank, H. Harbrecht, M. Hinze, R. Rannacher, and S. Ulbrich (Eds.), Trends in PDE Constrained Optimization, International Series of Numerical Mathematics, Vol. 165, pp. 173-188, Birkhäuser, Basel, 2014. [ISBN: 978-3-319-05082-9] DOI: 10.1007/978-3-319-05083-6_11 [BC15] A Robust Algorithm for Parametric Model Order Reduction Based on Implicit Moment Matching Peter Benner and Lihong Feng In A. Quarteroni and G. Rozza (Eds.), Reduced Order Methods for Modeling and Computational Reduction, MS&A - Modeling, Simulation and Applications, Vol. 9, pp. 159-185, Springer International Publishing, 2014. [ISBN: 978-1-4614-7550-7] DOI: 10.1007/978-3-319-02090-7_6 [BC14] Control Theory Peter Benner In Leslie Hogben (Ed.), Handbook of Linear Algebra, Second Edition, Chapter 80, Chapman & Hall/CRC, 2014. [ISBN: 978-1-4665-0728-9] Updated and revised version of BC8. [BC13] Computing Surrogates for Gas Network Simulation using Model Order Reduction Sara Grundel, Nils Hornung, Bernhard Klaassen, Peter Benner, and Tanja Clees In S. Koziel and L. Leifsson (Eds.), Surrogate-Based Modeling and Optimization, pp. 189-212, Springer-Verlag, 2013. [ISBN: 978-1-4614-7550-7] DOI: 10.1007/978-1-4614-7551-4_9 [BC12] Unleashing CPU-GPU Acceleration for Control Theory Applications Peter Benner, Pablo Ezzatti, Enrique S. Quintana-Ortí, and Alfredo Remón In I. Caragiannis et al. (Eds.), Euro-Par 2012, Parallel Processing Workshops., Lecture Notes in Computer Science, Vol. 7640, pp. 102-111, Springer-Verlag, Berlin/Heidelberg, 2013. [ISBN: 978-3-642-36948-3] DOI: 10.1007/978-3-642-36949-0_13 [BC11] System-Level Modeling of MEMS by Means of Model Order Reduction (Mathematical Approximations) - Mathematical Background Lihong Feng, Peter Benner, and Jan G. Korvink In T. Bechthold, G. Schrag, and L. Feng (Eds.), System-Level Modeling of MEMS, Advanced Micro & Nanosystems, Vol. 10, pp. 53-93, Wiley-VCH Verlag, Weinheim, Germany, 2013. [ISBN-13: 978-3-5273-1903-9] DOI: 10.1002/9783527647132.ch3 [BC10] Stabilization of Incompressible Flow Problems by Riccati-Based Feedback Eberhard Bänsch and Peter Benner In G. Leugering, S. Engell, A. Griewank, M. Hinze, R. Rannacher, V. Schulz, M. Ulbrich, and S. Ulbrich (Eds.), Constrained Optimization and Optimal Control for Partial Differential Equations, International Series of Numerical Mathematics, Vol. 160, pp. 5-20, Birkhäuser, Basel, 2012. DOI: 10.1007/978-3-0348-0133-1 [BC9] Partial Stabilization of Descriptor Systems Using Spectral Projectors Peter Benner In P. Van Dooren, S. Bhattacharyya, R. Chan, V. Olshevsky, and A. Routray (Eds.), Numerical Linear Algebra in Signals, Systems and Control, Lecture Notes in Electrical Engineering, Vol. 80, pp. 55-76, Springer-Verlag, Dordrecht, 2011. DOI: 10.1007/978-94-007-0602-6_3 [BC8] Control Theory Peter Benner In Leslie Hogben (Ed.), Handbook of Linear Algeba, Chapter 57, Chapman & Hall/CRC, 2006.[ISBN-13: 978-1-58488-510-8] [BC7] Numerical Solution of Optimal Control Problems for Parabolic Systems Peter Benner, Sabine Görner, and Jens Saak In K.-H. Hoffmann and A. Meyer (Eds.), Parallel Algorithms and Cluster Computing: Implementations, Algorithms and Applications, Vol. 52 of Lecture Notes in Computational Science and Engineering, pp. 151-169, Springer-Verlag, Berlin, Heidelberg, New York, 2006. [ISBN/ISSN: 3-540-33539-0] DOI: 10.1007/3-540-33541-2_9 [BC6] Model Reduction Based on Spectral Projection Methods Peter Benner and Enrique S. Quintana-Ortí In P. Benner, V. Mehrmann, and D.C. Sorensen (Eds.), Dimension Reduction of Large-Scale Systems, Ch. 1, Lecture Notes in Computational Science and Engineering, Vol. 45, pp. 5-48, Springer-Verlag, Berlin/Heidelberg, June 2005. DOI: 10.1007/3-540-27909-1_1 [BC5] A Semi-Discretized Heat Transfer Model for Optimal Cooling of Steel Profiles Peter Benner and Jens Saak In P. Benner, V. Mehrmann, and D.C. Sorensen (Eds.), Dimension Reduction of Large-Scale Systems, Ch. 19, Lecture Notes in Computational Science and Engineering, Vol. 45, pp. 353-356, Springer-Verlag, Berlin/Heidelberg, June 2005. DOI: 10.1007/3-540-27909-1_19 [BC4] Skew-Hamiltonian and Hamiltonian Eigenvalue Problems: Theory, Algorithms and Applications Peter Benner, Daniel Kressner, and Volker Mehrmann In Z. Drmač, M. Marušić, and Z. Tutek (Eds.), Proceedings of the Conference on Applied Mathematics and Scientific Computing, pp. 3-39. Springer-Verlag, 2005. [ISBN: 978-1-4020-3196-0] DOI: 10.1007/1-4020-3197-1_1 [BC3] A Model Reduction Web Environment for Very Large Linear Dynamical Systems Peter Benner, Rafael Mayo, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí In V.Y. Pan and L.T. Yang (Eds.), Parallel and Distributed Scientific and Engineering Computing: Practice and Experience, Advances in Computation: Theory and Practice, Vol. 15, pp. 23-33, NOVA Science Publishers, Hauppauge, NY, 2004. [ISBN:1-59033-956-8] [BC2] A Portable Subroutine Library for Solving Linear Control Problems on Distributed Memory Computers Peter Benner, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí In G. Cooperman, E. Jessen, and G.O. Michler (Eds.), Workshop on Wide Area Networks and High Performance Computing, Essen (Germany), September 1998, Lecture Notes in Control and Information, Vol. 249, pp. 61-87, Springer-Verlag, Berlin/Heidelberg, 1999. [ISBN: 1-85233-642-0] DOI: 10.1007/BFb0110079 The retrievable version is NICONET Report 1999-1, Working Group on Software, January 1999. [BC1] Numerical Methods for Linear Quadratic and H∞ Control Problems Peter Benner, Ralp Byers, Volker Mehrmann, and Hongguo Xu In G. Picci and D.S. Gilliam (Eds.), Dynamical Systems, Control, Coding, Computer Vision: New Trends, Interfaces, and Interplay, Vol. 25 of Progress in Systems and Control Theory, pp. 203-222, Birkhäuser, Basel, 1999. [ISBN: 978-3-0348-9848-5] DOI: 10.1007/978-3-0348-8970-4_10

## Technical reports

NOTE: The technical reports listed below either represent papers that will not be published elsewhere or longer versions of published articles (e.g., containing more algorithmic details or numerical examples).

 [TR34] SOMDDPA - Second-Order Modally-Damped Dominant Pole Algorithm (Version 1.0) Peter Benner and Steffen W. R. Werner DOI: 10.5281/zenodo.2553902 February 2019 [TR33] Limited Balanced Truncation for Large-Scale Sparse Second-Order Systems (Version 1.0) Peter Benner and Steffen W. R. Werner DOI: 10.5281/zenodo.2553926 February 2019 [TR32] MORLAB-4.0 - Model Order Reduction Laboratory Peter Benner and Steffen W. R. Werner DOI: 10.5281/zenodo.1574083 December 2018 [TR31] MORLAB-3.0 - Model Order Reduction Laboratory Peter Benner and Steffen W. R. Werner DOI: 10.5281/zenodo.842659 September 2017 [TR30] Example Setups of Navier-Stokes Equations with Control and Observation: Spatial Discretization and Representation via Linear-quadratic Matrix Coefficients Maximilian Behr, Peter Benner, and Jan Heiland arXiv e-print 1707.08711 [cs.MS] July 2017 [TR29] Balanced Truncation of Linear Time-Invariant Systems at a Single Frequency Xin Du, Peter Benner, Guanghong Yang, and Dan Ye MPI Magdeburg Preprint MPIMD/13-02, January 2013. [TR28] H2-Optimality Conditions for Structured Dynamical Systems Christopher Beattie and Peter Benner MPI Magdeburg Preprint MPIMD/14-18, October 2014. [TR27] Computational Solutions of a Family of Generalized Procrustes Problems Jens Fankhänel and Peter Benner Preprintreihe der Fakultät für Mathematik, Preprint 14-06, TU Chemnitz, June 2014. [TR26] Numerical Solution of Eigenvalue Problems for Alterating Matrix Polynomials and Their Application in Control Problems for Descriptor Systems Peter Benner, Philip Losse, Volker Mehrmann, and Matthias Voigt MPI Magdeburg Preprint MPIMD/13-24, December 2013. [TR25] FORTRAN 77 Subroutines for the Solution of Skew-Hamiltonian/Hamiltonian Eigenproblems - Part II: Implementation and Numerical Results Peter Benner, Matthias Voigt, and Vasile Sima SLICOT Working Note 2013-2, August 2013. [TR24] FORTRAN 77 Subroutines for the Solution of Skew-Hamiltonian/Hamiltonian Eigenproblems - Part I: Algorithms and Applications Peter Benner, Matthias Voigt, and Vasile Sima SLICOT Working Note 2013-1, August 2013. [TR23] Sparse-Dense Sylvester Equations in H2-Model Order Reduction Peter Benner, Martin Köhler, and Jens Saak MPI Magdeburg Preprint MPIMD/11-11, December 2011. [TR22] Model Predictive Control Based on an LQG Design for Time-Varying Linearizations Peter Benner and Sabine Hein Chemnitz Scientific Computing Preprints 09-07, TU Chemnitz, November 2009/March 2010. [TR21] A Galerkin-Newton-ADI Method for Solving Large-Scale Algebraic Riccati Equations Peter Benner and Jens Saak Preprint SPP1253-090, DFG Priority Programme 1253 Optimization with Partial Differential Equations, January 2010. [TR20] Projection-Based Model Reduction for Time-Varying Descriptor Systems: New Results Mohammad-Sahadet Hossain and Peter Benner MPI Magdeburg Preprint MPIMD/12-04, February 2012. [TR19] The SLICOT Toolboxes - a Survey Peter Benner, Daniel Kressner, Vasile Sima, and Andras Varga SLICOT Working Note 2009-1, August 2009. [TR18] Modellordnungsreduktion für strukturmechanische FEM-Modelle von Werkzeugmaschinen [German] Peter Benner Project Report, Chemnitz University of Technology, May 2008. [TR17] Balanced Truncation Model Reduction of Large and Sparse Generalized Linear Systems José M. Badía, Peter Benner, Rafael Mayo, Enrique S. Quintana-Ortí, Gregorio Quintana-Ortí, and Alfredo Remón Chemnitz Scientific Computing Preprints 06-04, TU Chemnitz, November 2006. [TR16] Solving Large-Scale Generalized Algebraic Bernoulli Equations via the Matrix Sign Function Sergio Barrachina, Peter Benner and Enrique S. Quintana-Ortí Preprint SFB393/05-15, Sonderforschungsbereich 393 - Numerische Simulation auf massiv parallelen Rechnern, TU Chemnitz, December 2005. [TR15] Linear-Quadratic Regulator Design for Optimal Cooling of Steel Profiles Peter Benner and Jens Saak Preprint SFB393/05-05, Sonderforschungsbereich 393 - Numerische Simulation auf massiv parallelen Rechnern, TU Chemnitz, April 2005. [TR14] Robust Numerical Methods for Robust Control Peter Benner, Ralph Byers, Volker Mehrmann, and Hongguo Xu Preprint 06-2004, Institut für Mathematik, TU Berlin, February 2004. [TR13] Experimental Evaluation of the Parallel Model Reduction Routines in PSLICOT Peter Benner, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí SLICOT Working Note 2002-7, August 2002. [TR12] Model Reduction Based on Iterative Solvers for Computing the System Gramians Peter Benner NICONET Newsletter, Vol. 8, pp. 5-7, 2002. [TR11] Schnelle Löser zur Berechnung elektromagnetischer Felder (in German) Peter Benner, Martin Brüning, and Angelika Bunse-Gerstner Project report, Zentrum für Technomathematik, Universität Bremen and EADS Bremen, March 2001. [TR10] Numerical Computation of Deflating Subspaces of Embedded Hamiltonian Pencils Peter Benner, Ralph Byers, Volker Mehrmann, and Hongguo Xu Preprint SFB393/99-15, Sonderforschungsbereich 393 - Numerische Simulation auf massiv parallelen Rechnern, TU Chemnitz, June 1999. [TR9] A Unified Deflating Subspace Approach for Classes of Polynomial and Rational Matrix Equations Peter Benner, Ralph Byers, Volker Mehrmann, and Hongguo Xu Preprint SFB393/00-05, Sonderforschungsbereich 393 - Numerische Simulation auf massiv parallelen Rechnern, TU Chemnitz, January 2000. [TR8] DAREX - A Collection of Benchmark Examples for Discrete-Time Algebraic Riccati Equations (Version 2.0) Jörn Abels and Peter Benner SLICOT Working Note 1999-16, December 1999. This report updates [TR2] [TR7] CAREX - A Collection of Benchmark Examples for Continuous-Time Algebraic Riccati Equations (Version 2.0) Jörn Abels and Peter Benner SLICOT Working Note 1999-14, November 1999. This report updates [TR1] [TR6] SLICOT Drives Tractors! Peter Benner and Heike Faßbender NICONET Newsletter, Vol. 2, pp. 17-22, 1999. See also: NICONET Report 1999-2, Working Group on Software, February 1999. [TR5] HAMEV and SQRED: Fortran 77 Subroutines for Computing the Eigenvalues of Hamiltonian Matrices Using Van Loans's Square Reduced Method Peter Benner, Ralph Byers, and Eric Barth Preprint SFB393/96-06, Sonderforschungsbereich 393 - Numerische Simulation auf massiv parallelen Rechnern, TU Chemnitz-Zwickau, May 1996. [TR4] A Restarted Symplectic Lanczos Method for the Hamiltonian Eigenvalue Problem Peter Benner and Heike Faßbender Technical Report SPC 95_28, TU Chemnitz-Zwickau, October 1995, Errata. [TR3] Newton's Method with Exact Line Search for Solving the Algebraic Riccati Equation Peter Benner and Ralph Byers Technical Report SPC 95_24, TU Chemnitz-Zwickau, October 1995. [TR2] A Collection of Benchmark Examples for the Numerical Solution of Algebraic Riccati Equations II: Discrete-Time Case Peter Benner, Alan J. Laub, and Volker Mehrmann Technical Report SPC 95_23, TU Chemnitz-Zwickau, Dezember 1995, Errata. [TR1] A Collection of Benchmark Examples for the Numerical Solution of Algebraic Riccati Equations I: Continuous-Time Case Peter Benner, Alan J. Laub, and Volker Mehrmann Technical Report SPC 95_22, TU Chemnitz-Zwickau, October 1995.

## Lecture notes

 [L3] Advanced Computational Methods for CACSD Peter Benner and Paul Van Dooren Tutorial workshop held at European Control Conference 2003, Cambridge, UK, September 1-4, 2003. Revised version June 22, 2004. [L2] Numerik für Ingenieure und Naturwissenschaftler (in German) Angelika Bunse-Gerstner, Peter Benner, and Heike Faßbender Zentrum für Technomathematik, Universität Bremen, Oktober 2000. [L1] Mathematik in der Berufspraxis (in German) Peter Benner (editor), Berichte aus der Technomathematik, Report 99-05, August 1999. Collection of protocols from a lecture series given by mathematicians from industry during the summer term 1998.

## Theses

 [T2] Contributions to the Numerical Solution of Algebraic Riccati Equations and Related Eigenvalue Problems Peter Benner Dissertation, Fakultät für Mathematik, TU Chemnitz-Zwickau, 1997. Published by Logos-Verlag, Berlin, June 1997 [ISBN: 3-931216-70-5]. Summary (in German). [T1] Ein orthogonal symplektischer Multishift Algorithms zur Lösung der algebraischen Riccatigleichung (in German) Peter Benner Diplomarbeit (Master's Thesis), Institut für Geometrie und Praktische Mathematik, RWTH Aachen, March 1993.

## Other publications

 [OP19] Die Rolle der GAMM beim Aufbau einer Nationalen Forschungsdateninfrastruktur Peter Benner and Stefan Diebels GAMM-Rundbrief 02/2019, 2019. [OP18] Drogen, Herbizide und numerische Simulation Peter Benner, Hermann Mena, and René Schneider Mitteilungen der Deutschen Mathematiker-Vereinigung, Vol. 23, No. 4, pp. 222–225, 2015. Translated to German from [OP12]. [OP17] Nanoelectronic COupled Problems Solutions - nanoCOPS E. Jan W. ter Maten, Piotr Putek, Michael Günther, Caren Tischendorf, Christian Strohm, Wim Schoenmaker, Peter Meuris, Bart De Smedt, Peter Benner, et al. Preprint BUW-IMACM 15/36, Bergische Universität Wuppertal, Germany, 2015. [OP16] The NanoCOPS Project on Algorithms for Nanoelectronic Coupled Problems Solutions R. Janssen, J. ter Maten, C. Tischendorf, H.-G. Brachtendorf, K. Bittner, W. Schoenmaker, P. Benner, L. Feng, R. Pulch, F. Deleu, and A. Wieers In B. Schrefler, E. Oñate, and M. Papadrakakis (Eds.), VI International Conference on Computational Methods for Coupled Problems in Science and Engineering, COUPLED Problems 2015, Venice, Italy, pp. 1029-1036, 2015. [OP15] nanoCOPS: Nanoelectronic COupled Problem Solutions P. Benner, K. Bittner, H.-G. Brachtendorf, H. De Gersen, F. Deleu, L. Feng, T. Götthans, M. Günther, R. Janssen, T. Kratochvíl, Q. Liu, P. Meuris, R. Pulch, P- Putek, P. Reynier, S. Schöps, J. Schneider, W. Schoenmaker, C. Strohm, E. Jan W. ter Maten, C. Tischendorf, and A. Wieers ECMI Newsletter, Vol. 56, pp. 62-67, 2014. [OP14] nanoCOPS: Parametric Modeling and Model Order Reduction of Coupled Problems Peter Benner, Lihong Feng, Peter Meuris, and Wim Schoenmaker ECMI Newsletter, Vol. 56, pp. 68-69, 2014. [OP13] Das Max-Planck-Institut für Dynamik komplexer technischer Systeme Peter Benner, Gabriele Ebel, Victoria Grimm, and Andreas Seidel-Morgenstern In G. Ihlow, H. Just, Ch. Kretzschmann, M. Maas, L. Modes, A. Neubauer, K. Pusch, H.-J. Rasehorn, R. Schmidt, J. Schulz, and J. Weschke (Eds.), Der Maschinen- und Anlagenbau in der Region Magdeburg zu Beginn des 21. Jahrhunderts, pp. 590-594, Verlag Delta-D, Magdeburg, 2014. [ISBN: 978-3-935831-51-2] [OP12] Drugs, Herbicides, and Numerical Simulation Peter Benner, Hermann Mena, and René Schneider Snapshots of Modern Mathematics from Oberwolfach, No. 10/2014, 9 pages, September 2014. [OP11] Compact Models for Simulation, Control and Optimization of Complex Dynamical Systems Peter Benner Yearbook 2011/12 of the Max Planck Society, May 2012. [OP10] Modeling and Optimal Control of Chemical Mechanical Planarization Susan Dürigen, Peter Benner, Uwe Stöckgen, and Jens Heinrich In T. Lery, M. Primicerio, M.J. Esteban, M. Fontes, Y. Maday, V. Mehrmann, G. Quadros, W. Schilders, A. Schuppert, and H. Tewkesbury (Eds.), European Success Stories in Industrial Mathematics, p. 76, Springer-Verlag, Berlin/Heidelberg, 2011. [ISBN: 978-3-642-23847-5] [OP9] O-MOORE-NICE! New methodologies and algorithms for design and simulation of analog integrated circuits Joost Rommes, Davit Harutyunyan, Michael Striebel, Luciano De Tommasi, Jan ter Maten, Peter Benner, Tom Dhaene, Wil Schilders, and Marcel Sevat ECMI Newsletter, Vol. 47, pp. 17-20, 2010. [OP8] The GAMM Activity Group Applied and Numerical Linear Algebra Peter Benner and Daniel Kressner IMAGE (Bulletin of the ILAS), Vol. 43, pp. 25-26, 2009. [OP7] System Reduction for Nanoscale IC Design (SyreNe) Peter Benner ECMI Newsletter, Vol. 45, pp. 18-21, 2009. [OP6] Model Reduction at ICIAM '07 Peter Benner SIAM News, Vol. 40, No. 8, pp. 16-17, October 2007. [OP5] Model Reduction using Center and Inertial Manifolds Peter Benner Berlin-Braunschweig-Chemnitz Workshop Recent Advances in Model Reduction, TU Chemnitz, 27 November 2006. [OP4] NICONET participation in the 7th European Control Conference, ECC03, University of Cambridge, UK, September 1-4, 2003 Peter Benner NICONET Newsletter, Vol. 11, pp. 5-8, 2003. [OP3] The freeware numerical subroutine library SLICOT for systems and control theory Ad van den Boom, Vasile Sima, Peter Benner, and Sabine Van Huffel Abstracts 17-th Benelux Meeting on Systems and Control, Mierlo, The Netherlands, March 1998. (!WinWord document!) [OP2] NICONET - Ein europäisches Netzwerk zur Numerik in der Kontrolltheorie (in German) Peter Benner Kopien der Vortragsfolien, Gemeinsamer Workshop GAMM-Fachausschuß "Dynamik und Regelungstheorie" und VDI/VDE-GMA Ausschuß 1.4 "Theoretische Verfahren der Regelungstechnik", Kassel, March 2-3, 1998, pp. 185-193. [OP1] Collections of Benchmark Examples in Control Peter Benner and Volker Mehrmann WGS Newsletter, Vol. 10, pp. 7-8, 1996.
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Peter Benner, benner@mpi-magdeburg.mpg.de