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.

[J263]  [new] Compact Thermo-Mechanical Models for the Fast Simulation of Machine Tools with Nonlinear Component Behavior
Julia Vettermann, Alexander Steinert, Christian Brecher, Peter Benner, and Jens Saak
at-Automatisierungstechnik, accepted 7 July 2022.
[J262]  [new] Model Order Reduction for Delayed PEEC Models With Guaranteed Accuracy and Observed Stability
Lihong Feng, Luigi Lombardi, Peter Benner, Daniele Romano, and Giulio Antonini
IEEE Transactions on Circuits and Systems I: Regular Papers, 14 pages, published online 14 July 2022.
DOI: 10.1109/TCSI.2022.3189389
[J261]  [new] Discovery of Nonlinear Dynamical Systems using a Runge-Kutta Inspired Dictionary-based Sparse Regression Approach
Pawan Goyal and Peter Benner
Proceedings of the Royal Society A, Vol. 478, Art. 20210883 (24 pages), 2022.
DOI: 10.1098/rspa.2021.0883
Preliminary version appeared as arXiv Preprint arXiv: 2105.04869, [cs.LG], May 2021.
[J260]  [new] A Low-Rank Solution Method for Riccati Equations with Indefinite Quadratic Terms
Peter Benner, Jan Heiland, and Steffen W. R. Werner
Numerical Algorithms, 21 pages, published online 31 May 2022.
DOI: 10.1007/s11075-022-01331-w
Preliminary version appeared as arXiv Preprint arXiv: 2111.06516, [math.NA], 12 November 2021.
[J259]  [new] Palindromic Linearization and Numerical Solution of Nonsymmetric Algebraic T-Riccati Equations
Peter Benner, Bruno Iannazzo, Beatrice Meini, and Davide Palitta
BIT Numerical Mathematics, published online 20 May 2022.
DOI: 10.1007/s10543-022-00926-y
Preliminary version appeared as arXiv Preprint arXiv: 2110.03254, [math.NA], 7 October 2021.
[J258]  [new] Reduced Basis Method for the Nonlinear Poisson-Boltzmann Equation regularized by the Range-Separated Canonical Tensor Format
Cleophas Kweyu, Lihong Feng, Matthias Stein, and Peter Benner
International Journal of Nonlinear Sciences and Numerical Simulation, published online 18 May 2022.
DOI: 10.1515/ijnsns-2021-0103
Preliminary version appeared as arXiv Preprint arXiv:2103.00245, [math.NA], February 2021.
[J257]  [new] Convergence Analysis of Vector Extended LOBPCG for Computing Extreme Eigenvalues
Peter Benner and Xin Liang
Numerical Linear Algebra with Applications, e2445 (24 pages), published online 9 May 2022.
DOI: 10.1002/nla.2445
Preliminary version appeared as arXiv Preprint arXiv:2004.14002v1, [math.NA], April 2020.
[J256] Convolutional Neural Networks for Very Low-dimensional LPV Approximations of Incompressible Navier-Stokes Equations
Jan Heiland, Peter Benner, and Rezvan Bahmani
Frontiers in Applied Mathematics and Statistics, section Statistical and Computational Physics, published online 29 April 2022.
DOI: 10.3389/fams.2022.879140
[J255] A Greedy Data Collection Scheme For Linear Dynamical Systems
Karim Cherifi, Pawan Goyal, and Peter Benner
Data-Centric Engineering, Vol. 3, e16 (14 pages), 2022.
DOI: 10.1017/dce.2022.16
Preliminary version appeared as arXiv Preprint arXiv: 2107.12950, [eess.SY], 27 July 2021.
[J254] Stable and Efficient Computation of Generalized Polar Decompositions
Peter Benner, Yuji Nakatsukasa, and Carolin Penke
SIAM Journal on Matrix Analysis and Applications, accepted 7 March 2022.
Preliminary version appeared as arXiv Preprint arXiv:2104.06659, [math.NA], April 2021.
[J253] Robust Output-Feedback Stabilization for Incompressible Flows using Low-Dimensional H-Controllers
Peter Benner, Jan Heiland, and Steffen W. R. Werner
Computational Optimization and Application, published online, 2022.
DOI: 10.1007/s10589-022-00359-x
Preliminary version appeared as arXiv Preprint arXiv:2103.01608, [math.OC], March 2021.
[J252] Fast A Posteriori State Error Estimation for Reliable Frequency Sweeping in Microwave Circuits via the Reduced-Basis Method
Valentin de la Rubia, Sridhar Chellappa, Lihong Feng, and Peter Benner
IEEE Transactions on Microwave Theory and Techniques, accepted 17 January 2022.
Preliminary version appeared as arXiv Preprint arXiv: 2110.05925, [math.NA], 12 October 2021.
[J251] Parallel Algorithms for Tensor Train Arithmetic
Hussam Al Daas, Grey Ballard, and Peter Benner
SIAM Journal on Scientific Computing, Vol. 44, Issue 1, pp. C25-C35, 2022.
DOI: 10.1137/20M1387158
Preliminary version appeared as arXiv Preprint arXiv:2011.06532, [math.NA], November 2020.
[J250] A Training Set Subsampling Strategy for the Reduced Basis Method
Sridhar Chellappa, Lihong Feng, and Peter Benner
Journal of Scientific Computing, Vol. 89, Art. 63 (pp. 34), 2021.
DOI: 10.1007/s10915-021-01665-y
Preliminary version appeared as arXiv Preprint arXiv:2103.06185, [math.NA], March 2021.
[J249] A Non-Intrusive Method to Inferring Linear Port-Hamiltonian Realizations using Time-Domain Data
Karim Cherifi, Pawan Goyal, and Peter Benner
Electronic Transactions on Numerical Analysis, (Special Volume on Scientific Machine Learning), Vol. 56, pp. 102-116, 2022.
DOI: 10.1553/etna_vol56s102
Preliminary version appeared as arXiv Preprint arXiv:2005.09371, [eess.SY], May 2020.
[J248] Data-Driven Model Order Reduction for Problems with Parameter-Dependent Jump-Discontinuities
Neeraj Sarna and Peter Benner
Computer Methods in Applied Mechanics and Engineering, Vol. 387, Art. 114168, 2021.
DOI: 10.1016/j.cma.2021.114168
Preliminary version appeared as arXiv Preprint arXiv:2105.00547, [math.NA], May 2021.
[J247] Index-Aware Model-Order Reduction for a Special Class of Nonlinear Differential-Algebraic Equations
Nicodemus Banagaaya, Giuseppe Ali, Sara Grundel, and Peter Benner
Journal of Dynamics and Differential Equations, published online, 2021.
DOI: 10.1007/s10884-021-10063-9
Preliminary version appeared as arXiv Preprint arXiv:2002.09751v1, [math.NA], February 2020.
[J246] Model Order Reduction Methods for Coupled Machine Tool Models
Julia Vettermann, Stefan Sauerzapf, Andreas Naumann, Michael Beitelschmidt, Roland Herzog, Peter Benner, and Jens Saak
MM Science Journal, pp. 4652-4659, 2021.
DOI: 10.17973/MMSJ.2021_7_2021072
[J245] Model Order Reduction for Gas and Energy Networks
Christian Himpe, Sara Grundel, and Peter Benner
Journal of Mathematics in Industry, Vol. 11, Art. 13 (pp. 46), 2021.
DOI: 10.1186/s13362-021-00109-4
Preliminary version appeared as arXiv Preprint arXiv:2011.12099, [math.OC], November 2020.
[J244] NFDI for Catalysis-Related Sciences: NFDI4Cat
Sara Espinoza, David Linke, Christoph Wulf, Sonja Schimmler, Stephan Andreas Schunk, Peter Benner et al.
Bausteine Forschungsdatenmanagement, pp. 57-71, 2021.
DOI: 10.17192/bfdm.2021.2.8333
[J243] Gramians, Energy Functionals and Balanced Truncation for Linear Dynamical Systems with Quadratic Outputs
Peter Benner, Pawan Goyal, and Igor Pontes Duff
IEEE Transactions on Automatic Control, Vol 67, Issue 2, pp. 886-893, 2022.
DOI: 10.1109/TAC.2021.3086319
Preliminary version appeared as arXiv Preprint arXiv:1909.04597v1, [math.OC], September 2019.
[J242] A Stochastic Maximum Principle for Control Problems Constrained by the Stochastic Navier-Stokes Equations
Peter Benner and Christoph Trautwein
Applied Mathematics and Optimization, Vol. 84, pp. 1001-1054, 2021.
DOI: 10.1007/s00245-021-09792-6
Preliminary version appeared as arXiv Preprint arXiv:1810.12119[math.OC], October 2018.
[J241] Efficient and Accurate Algorithms for Solving the Bethe-Salpeter Eigenvalue Problem for Crystalline Systems
Peter Benner and Carolin Penke
Journal of Computational and Applied Mathematics, Vol. 400, Art. 113650, 2022.
DOI: 10.1016/j.cam.2021.113650
Preliminary version appeared as arXiv Preprint arXiv:2008.08825, [math.NA], August 2020.
[J240] Galerkin Trial Spaces and Davison-Maki Methods for the Numerical Solution of Differential Riccati Equations
Maximilian Behr, Peter Benner, and Jan Heiland
Applied Mathematics and Computation, Vol. 410, Art. 126401 (28 pp.), 2021.
DOI: 10.1016/j.amc.2021.126401
Preliminary version appeared as arXiv Preprint arXiv:1910.13362, [math.NA], October 2019.
[J239] Learning Reduced-order Dynamics for Parametrized Shallow Water Equations from Data
Süleyman Yildiz, Pawan Goyal, Peter Benner, and Bülent Karasözen
International Journal for Numerical Methods in Fluids, Vol. 93, Issue 8, pp. 2803-2821, 2021.
DOI: 10.1002/fld.4998
Preliminary version appeared as arXiv Preprint arXiv:2007.14079, [math.NA, July 2020.
[J238] Structure-Preserving Interpolation for Model Reduction of Parametric Bilinear Systems
Peter Benner, Serkan Gugercin, and Steffen W. R. Werner
Automatica, Vol. 132, Art. 109799 (9 pp.), 2021.
DOI: 10.1016/j.automatica.2021.109799
Preliminary version appeared as arXiv Preprint arXiv:2007.11269, [math.NA], July 2020.
[J237] A Rational Even-IRA Algorithm for the Solution of T-even Polynomial Eigenvalue Problems
Peter Benner, Heike Fassbender, and Philip Saltenberger
SIAM Journal on Matrix Analysis and Applications, Vol. 42, Issue 3, pp. 1172-1198, 2021.
DOI: 10.1137/20M1364485
Preliminary version appeared as arXiv Preprint arXiv:2009.01762, [math.NA], September 2020.
[J236] Operator Inference and Physics-Informed Learning of Low-Dimensional Models for Incompressible Flows
Peter Benner, Pawan Goyal, Jan Heiland, and Igor Pontes Duff
Electronic Transactions on Numerical Analysis, (Special Volume on Scientific Machine Learning), Vol. 56, pp. 28-51, 2022.
DOI: 10.1553/etna_vol56s28
Preliminary version appeared as arXiv Preprint arXiv:2010.06701, [math.DS], October 2020.
[J235] A Linear Implicit Euler Method for the Finite Element Discretization of a Controlled Stochastic Heat Equation
Peter Benner, Tony Stillfjord, and Christoph Trautwein
IMA Journal of Numerical Analysis, published online, 2021.
DOI: 10.1093/imanum/drab033
Preliminary version appeared as arXiv Preprint arXiv:2006.05370, [math.NA], June 2020.
[J234] Structure-Preserving Interpolation of Bilinear Control Systems
Peter Benner, Serkan Gugercin, and Steffen W. R. Werner
Advances in Computational Mathematics, Vol. 47, Issue 3, Art. 43 (38 pp.), 2021.
DOI: 10.1007/s10444-021-09863-w
Preliminary version appeared as arXiv Preprint arXiv:2005.00795v1, [math.NA], May 2020.
[J233] Relative Perturbation Theory for Quadratic Hermitian Eigenvalue Problem
Peter Benner, Xin Liang, Suzana Miodragović, and Ninoslav Truhar
Linear Algebra and its Applications, Vol. 618, pp. 97-128, 2021.
DOI: 10.1016/j.laa.2021.01.023
Preliminary version appeared as arXiv Preprint arXiv:1602.03420v2 [math.NA], February 2016.
[J232] Factorized Solution of Generalized Stable Sylvester Equations Using Many-Core GPU Accelerators
Peter Benner; Ernesto Dufrechou; Pablo Ezzatti; Rodrigo Gallardo; Enrique Quintana-Ortí
Journal of Supercomputing, Vol. 77, pp. 10152-10164, 2021.
DOI: 10.1007/s11227-021-03658-y
[J231] Tomographic X-ray Scattering based on Invariant Reconstruction - Analysis of the 3D Nanostructure of Bovine Bone
Paolino De Falco, Richard Weinkamer, Wolfgang Wagermaier, Chenghao Li, Tim Snow, Nicholas J. Terrill, Himadri S. Gupta, Pawan Goyal, Martin Stoll, Peter Benner and Peter Fratzl
Journal of Applied Crystallography, Vol. 54, pp. 486-497, 2021.
DOI: 10.1107/S1600576721000881
[J230] On Error Estimation for Reduced-Order Modeling of Linear Non-Parametric and Parametric Systems
Lihong Feng and Peter Benner
ESAIM: Mathematical Modelling and Numerical Analysis (M2AN), Vol. 55, Issue 2, pp. 561-594, 2021.
DOI: 10.1051/m2an/2021001
Preliminary version appeared as arXiv Preprint arXiv:2003.14319, [math.NA], March 2020.
[J229] Regularization of Poisson-Boltzmann Type Equations with Singular Source Terms using the Range-Separated Tensor Format
Peter Benner, Boris Khoromskij, Venera Khoromskaia, Cleophas Kweyu, and Matthias Stein
SIAM Journal on Scientific Computing, Vol. 43, Issue 1, pp. A415-A445, 2021.
DOI: 10.1137/19M1281435
Preliminary version appeared as arXiv Preprint arXiv:1901.09864, [math.NA], January 2019.
[J228] Implicit Higher-Order Moment Matching Technique for Model Reduction of Quadratic-bilinear Systems
Mian Muhammad Arsalan Asif, Mian Ilyas Ahmad, Peter Benner, Lihong Feng, and Tatjana Stykel
Journal of the Franklin Institute, Vol. 358, Issue 3, pp. 2015-2038, 2021.
DOI: 10.1016/j.jfranklin.2020.11.012
Preliminary version appeared as arXiv Preprint arXiv:1911.05400, [eess.SY], November 2019.
[J227] Machine Learning for Material Characterization with an Application for Predicting Mechanical Properties
Anke Stoll and Peter Benner
GAMM Mitteilungen, Vol. 44, Issue 1, e202100003 (21 pp.), 2021.
DOI: 10.1002/gamm.202100003
Preliminary version appeared as arXiv Preprint arXiv:2010.06010, [cs.LG], October 2020.
[J226] Balanced Truncation of Linear Time-Invariant Systems over Finite-frequency Ranges
Peter Benner, Xin Du, Guanghong Yang, and Dan Ye
Advances in Computational Mathematics, Vol. 46, Art. 82 (34 pp.), 2020.
DOI: 10.1007/s10444-020-09823-w
Preliminary version appeared as arXiv Preprint arXiv:1602.04402v1 [cs.SY], February 2016.
[J225] Interpolation-Based Model Order Reduction for Polynomial Systems
Peter Benner and Pawan Goyal
SIAM Journal on Scientific Computing, Vol. 43, Issue 1, A84-A108, 2021.
DOI: 10.1137/19M1259171
Preliminary version appeared as arXiv Preprint arXiv:1904.11891, [math.NA], April 2019.
[J224] On the Solution of the Nonsymmetric T-Riccati Equation
Peter Benner and Davide Palitta
Electronic Transactions on Numerical Analysis (ETNA), Vol. 54, pp. 68-88, 2021.
DOI: 10.1553/etna_vol54s68
Preliminary version appeared as arXiv Preprint arXiv:2003.03693v1, [math.NA], March 2020.
[J223] Model Order Reduction for Delay Systems by Iterative Interpolation
Dominik Alfke, Lihong Feng, Luigi Lombardi, Giulio Antonini, and Peter Benner
International Journal for Numerical Methods in Engineering, Vol. 122, Issue 3, pp. 684-706, 2021.
DOI: 10.1002/nme.6554
[J222] Operator Inference for Non-Intrusive Model Reduction of Systems with Non-Polynomial Nonlinear Terms
Peter Benner, Pawan Goyal, Boris Kramer, Benjamin Peherstorfer, and Karen Willcox
Computer Methods in Applied Mechanics and Engineering, Vol. 372, 113433 (17 pp.), 2020.
DOI: 10.1016/j.cma.2020.113433
Preliminary version appeared as arXiv Preprint arXiv:2002.09726, [math.NA], February 2020.
[J221] Fast Solution of the Linearized Poisson-Boltzmann Equation with nonaffine Parametrized Boundary Conditions Using the Reduced Basis Method
Cleophas Kweyu, Lihong Feng, Matthias Stein, and Peter Benner
Computing and Visualization in Science, Vol. 23, Art. 15 (19 pp.), 2020.
DOI: 10.1007/s00791-020-00336-z
Preliminary version appeared as arXiv Preprint arXiv:1705.08349, May 2017.
[J220] Efficient Numerical Methods for Gas Network Modeling and Simulation
Yue Qiu, Sara Grundel, Martin Stoll, and Peter Benner
Networks and Heterogeneous Media, Vol. 15, Issue 4, pp. 653-679, 2020.
DOI: 10.3934/nhm.2020018
Preliminary version appeard as arXiv Preprint arXiv:1807.07142 [math.NA], July 2018.
[J219] Identification of Port-Hamiltonian Systems from Frequency Response Data
Peter Benner, Pawan Goyal, and Paul Van Dooren
Systems & Control Letters, Vol. 143, 104741 (9 pp.), 2020.
DOI: 10.1016/j.sysconle.2020.104741
Preliminary version appeared as arXiv Preprint arXiv:1911.00080v1, [eess.SY], October 2019.
[J218] Frequency- and Time-Limited Balanced Truncation for Large-Scale Second-Order Systems
Peter Benner and Steffen W. R. Werner
Linear Algebra and Its Applications, Special Issue in Honor of Paul Van Dooren, Vol. 623, pp. 68-103, 2021.
DOI: 10.1016/j.laa.2020.06.024
Preliminary version appeared as arXiv Preprint arXiv:2001.06185, [math.OC], January 2020.
[J217] Low-Rank Linear Fluid-Structure Interaction Discretizations
Roman Weinhandl, Peter Benner, and Thomas Richter
Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM), Vol. 100, Issue 11, e201900205 (28 pp.), 2020. [Editor's Choice]
DOI: 10.1002/zamm.201900205
Preliminary version appeared as arXiv Preprint arXiv:1905.11000, [math.NA], May 2019.
[J216] Adaptive Basis Construction and Improved Error Estimation for Parametric Nonlinear Dynamical Systems
Peter Benner, Sridhar Chellappa, and Lihong Feng
International Journal for Numerical Methods in Engineering, Vol. 121, Issue 23, pp. 5320-5349, 2020.
DOI: 10.1002/nme.6462
Preliminary version appeared as arXiv Preprint arXiv:1911.05235, [math.NA], November 2019.
[J215] High Performance Solution of Skew-symmetric Eigenvalue Problems with Applications in Solving the Bethe-Salpeter Eigenvalue Problem
Carolin Penke, Andreas Marek, Christian Vorwerk, Claudia Draxl, and Peter Benner
Parallel Computing, Vol. 96, Art. 102639 (8 pp.), 2020.
Preliminary version appeared as arXiv Preprint arXiv:1912.04062v1, [math.NA], December 2019.
[J214] Low-Rank Solution of an Optimal Control Problem Constrained by Random Navier-Stokes Equations
Peter Benner, Sergey Dolgov, Akwum Onwunta, and Martin Stoll
International Journal for Numerical Methods in Fluids, Vol. 92, Issue 11, pp. 1653-1678, 2020.
DOI: 10.1002/fld.4843
Preliminary version appeared as arXiv Preprint arXiv:1703.06097, [math.NA], March 2017.
[J213] A Subspace Framework for H-Norm Minimization
Nicat Aliyev, Peter Benner, Emre Mengi, and Matthias Voigt
SIAM Journal on Matrix Analysis and Applications, Vol. 41, Issue 2, pp. 928–956, 2020.
DOI: 10.1137/19M125892X
Preliminary version appeared as arXiv Preprint arXiv:1905.04208, [math.NA], May 2019.
[J212] Model Order Reduction for Bilinear Control Systems with Inhomogeneous Initial Conditions
Xingang Cao, Peter Benner, Igor Pontes Duff, and Wil Schilders
International Journal of Control, Vol. 94, Issue 10, pp. 2886-2895, 2021.
DOI: 10.1080/00207179.2020.1740945
[J211] A Numerical Comparison of Different Solvers for Large-Scale, Continuous-Time Algebraic Riccati Equations and LQR Problems
Peter Benner, Zvonimir Bujanović, Patrick Kürschner, and Jens Saak
SIAM Journal on Scientific Computing, Vol 42, Issue 2, pp. A957-A996, 2020.
DOI: 10.1137/18M1220960
Preliminary version appeared as arXiv Preprint arXiv:1811.00850[math.NA], November 2018.
[J210] Hankel-Norm Approximation of Large-Scale Descriptor Systems
Peter Benner and Steffen W. R. Werner
Advances in Computational Mathematics, Vol. 46, Issue 3, Article 40 (31 pp.), 2020.
DOI: 10.1007/s10444-020-09750-w
Preliminary version appeared as arXiv Preprint arXiv:1612.06205v2, [math.OC], December 2018.
[J209] 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
Applied Numerical Mathematics, Vol. 152, pp. 338-354, 2020.
DOI: 10.1016/j.apnum.2019.11.016
Preliminary version appeared as arXiv Preprint arXiv:1804.01410[math.NA], April 2018.
[J208] Solution Formulas for Differential Sylvester and Lyapunov Equations
Maximilian Behr, Peter Benner, and Jan Heiland
Calcolo, Vol. 56, Article 51 (33 pp.), 2019.
DOI: 10.1007/s10092-019-0348-x
Preliminary version appeared as arXiv Preprint arXiv:1811.08327[math.NA], November 2018.
[J207] Greedy Low-Rank Algorithm for Spatial Connectome Regression
Patrick Kürschner, Sergey Dolgov, Kameron Decker Harris, and Peter Benner
The Journal of Mathematical Neuroscience, Vol. 9, Issue 1, Article 9 (22 pp.), 2019.
DOI: 10.1186/s13408-019-0077-0
Preliminary version appeared as arXiv Preprint arXiv:1808.05510[math.NA], August 2018.
[J206] A New Error Estimator for Reduced-Order Modeling of Linear Parametric Systems
Lihong Feng and Peter Benner
IEEE Transactions on Microwave Theory and Techniques, Vol. 67, Issue 12, pp. 4848-4859, 2019.
DOI: 10.1109/TMTT.2019.2948858
[J205] Cross-Gramian-Based Dominant Subspaces
Peter Benner and Christian Himpe
Advances in Computational Mathematics, Vol. 45, Issue 5, pp. 2533-2553, 2019.
DOI: 10.1007/s10444-019-09724-7
Preliminary version appeared as arXiv Preprint arXiv:1809.08066[math.OC], September 2018.
[J204] Extended and Improved Criss-Cross Algorithms for Computing the Spectral Value Set Abscissa and Radius
Peter Benner and Tim Mitchell
SIAM Journal on Matrix Analysis and Applications, Vol. 40, Issue 4, pp. 1325-1352, 2019.
DOI: 10.1137/19M1246213
Preliminary version appeared as arXiv Preprint arXiv:1712.10067 [math.OC], December 2017.
[J203] Model Reduction of Controlled Fokker-Planck and Liouville-von Neumann Equations
Peter Benner, Tobias Breiten, Carsten Hartmann, and Burkhard Schmidt
Journal of Computational Dynamics, Vol. 7, Issue 1, pp. 1-33, 2020.
DOI: 10.3934/jcd.2020001
Preliminary version appeared as arXiv Preprint arXiv:1706.09882 , July 2017.
[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, Vol. 65, Issue 6, pp. 2526-2535, 2020.
DOI: 10.1109/TAC.2019.2934020
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, Vol. 6, Art. 10 (33 pp.), 2019.
DOI: 10.1186/s40323-019-0134-y
[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, Vol. 26, Art. 62 (32 pp.), 2020.
DOI: 10.1051/cocv/2019042
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, Vol. 45, Issue 5-6. pp. 2241–2271, 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, Vol. 382, pp. 221-239, 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 (38 pp.), 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 (12 pp.), 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
Athanasios C. Antoulas, Peter Benner, and Lihong Feng
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 (23 pp.), 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 (16 pp.), 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 (19 pp.), 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 (13 pp.), 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 (26 pp.), 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 pp.), 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 ℋ-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.