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Mathematical and Computer Modelling of Dynamical Systems
Methods, Tools and Applications in Engineering and Related Sciences
Volume 19, 2013 - Issue 6
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Original Articles

An improved numerical method for balanced truncation for symmetric second-order systems

Peter BennerComputational Methods in Systems and Control Theory, Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany
,
Patrick KürschnerComputational Methods in Systems and Control Theory, Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, GermanyCorrespondence[email protected]
&
Jens SaakComputational Methods in Systems and Control Theory, Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany
Pages 593-615 | Received 09 Nov 2012, Accepted 06 Apr 2013, Published online: 01 May 2013

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Md Saiduzzaman, Md Shafiqul Islam, Mohammad Monir Uddin & Mohammad Osman Gani. (2022) Comparative study on techniques of model order reduction using rational Krylov subspace method. Journal of Interdisciplinary Mathematics 25:7, pages 1971-1978.
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Peter Benner, Roland Herzog, Norman Lang, Ilka Riedel & Jens Saak. (2019) Comparison of model order reduction methods for optimal sensor placement for thermo-elastic models. Engineering Optimization 51:3, pages 465-483.
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Peter Benner, Jens Saak & M. Monir Uddin. (2016) Structure preserving model order reduction of large sparse second-order index-1 systems and application to a mechatronics model. Mathematical and Computer Modelling of Dynamical Systems 22:6, pages 509-523.
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T. Wolf & H.K.F. Panzer. (2016) The ADI iteration for Lyapunov equations implicitly performs pseudo-optimal model order reduction. International Journal of Control 89:3, pages 481-493.
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Articles from other publishers (31)

Paul Schwerdtner & Matthias Voigt. (2023) SOBMOR: Structured Optimization-Based Model Order Reduction. SIAM Journal on Scientific Computing 45:2, pages A502-A529.
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Malte Wrobel & Thomas Meurer. (2023) Optimal sensor placement and estimator-based temperature control for a deep drawing process. Journal of Process Control 124, pages 92-104.
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Mahtab Uddin, M. Monir Uddin & Md. Abdul Hakim Khan. (2023) SVD-Krylov-based sparsity-preserving techniques to optimally stabilize the incompressible Navier–Stokes flows. International Journal of Dynamics and Control.
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Joel D. Simard, Xiaodong Cheng & Alessio Moreschini. (2023) Interpolants With Second-Order Structure in the Loewner Framework. IFAC-PapersOnLine 56:2, pages 4278-4283.
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Mahtab Uddin, Md. Toriqul Islam, M. Monir Uddin & M. A. Hakim Khan. (2022) Riccati-based feedback stabilization of incompressible Navier-Stokes models via reduced-order modelling by iterative rational Krylov algorithm. Riccati-based feedback stabilization of incompressible Navier-Stokes models via reduced-order modelling by iterative rational Krylov algorithm.
Md. Toriqul Islam, Mahtab Uddin, M. Monir Uddin, Md. Abdul Hakim Khan & Md. Tanzim Hossain. (2022) Sparsity-Preserving Two-Sided Iterative Algorithm for Riccati-Based Boundary Feedback Stabilization of the Incompressible Navier–Stokes Flow. Mathematical Problems in Engineering 2022, pages 1-14.
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Akbar Shirilord & Mehdi Dehghan. (2022) Closed-form solution of non-symmetric algebraic Riccati matrix equation. Applied Mathematics Letters 131, pages 108040.
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Johanna Kerler-Back & Tatjana Stykel. 2022. Realization and Model Reduction of Dynamical Systems. Realization and Model Reduction of Dynamical Systems 273 297 .
Christian Bertram & Heike Faßbender. (2021) A quadrature framework for solving Lyapunov and Sylvester equations. Linear Algebra and its Applications 622, pages 66-103.
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Md. Motlubar Rahman, M. Monir Uddin, L. S. Andallah & Mahtab Uddin. (2020) Tangential interpolatory projections for a class of second-order index-1 descriptor systems and application to Mechatronics. Production Engineering 15:1, pages 9-19.
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Patrick Kürschner & Melina A. Freitag. (2020) Inexact methods for the low rank solution to large scale Lyapunov equations. BIT Numerical Mathematics 60:4, pages 1221-1259.
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M. Monir Uddin. (2020) Structure preserving model order reduction of a class of second-order descriptor systems via balanced truncation. Applied Numerical Mathematics 152, pages 185-198.
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Md. Motlubar Rahman, Mohammad Monir Uddin, Laek Sazzad Andallah & Mahtab Uddin. (2020) Interpolatory Projection Techniques for H2 Optimal Structure-Preserving Model Order Reduction of Second-Order Systems. Advances in Science, Technology and Engineering Systems Journal 5:4, pages 715-723.
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Jens Saak, Dirk Siebelts & Steffen W. R. Werner. (2019) A comparison of second-order model order reduction methods for an artificial fishtail. at - Automatisierungstechnik 67:8, pages 648-667.
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M. Monir Uddin. (2018) Gramian‐based model‐order reduction of constrained structural dynamic systems. IET Control Theory & Applications 12:17, pages 2337-2346.
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Maxime Thieffry, Alexandre Kruszewski, Thierry-Marie Guerra & Christian Duriez. (2018) Reduced Order Control of Soft Robots with Guaranteed Stability. Reduced Order Control of Soft Robots with Guaranteed Stability.
Peter Benner, Zvonimir Bujanović, Patrick Kürschner & Jens Saak. (2017) RADI: a low-rank ADI-type algorithm for large scale algebraic Riccati equations. Numerische Mathematik 138:2, pages 301-330.
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Johanna Kerler-Back & Tatjana Stykel. (2017) Model reduction for linear and nonlinear magneto-quasistatic equations. International Journal for Numerical Methods in Engineering 111:13, pages 1274-1299.
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Mohammad-Sahadet Hossain & M. Monir Uddin. (2017) Efficient Techniques for Solving the Periodic Projected Lyapunov Equations and Model Reduction of Periodic Systems. Mathematical Problems in Engineering 2017, pages 1-11.
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Peter Benner & Tatjana Stykel. 2017. Surveys in Differential-Algebraic Equations IV. Surveys in Differential-Algebraic Equations IV 107 160 .
Thomas Wolf, Heiko K.F. Panzer & Boris Lohmann. (2016) ADI iteration for Lyapunov equations: A tangential approach and adaptive shift selection. Applied Numerical Mathematics 109, pages 85-95.
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Peter Benner, Matthias Heinkenschloss, Jens Saak & Heiko K. Weichelt. (2016) An inexact low-rank Newton–ADI method for large-scale algebraic Riccati equations. Applied Numerical Mathematics 108, pages 125-142.
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Tatjana Stykel & Alexander Vasilyev. (2016) A two-step model reduction approach for mechanical systems with moving loads. Journal of Computational and Applied Mathematics 297, pages 85-97.
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M. Uddin, Jens Saak & Peter Benner. (2016) Balancing based model reduction for structured index-2 unstable descriptor systems with application to flow control. Numerical Algebra, Control and Optimization 6:1, pages 1-20.
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Norman Lang, Hermann Mena & Jens Saak. (2015) On the benefits of the factorization for large-scale differential matrix equation solvers . Linear Algebra and its Applications 480, pages 44-71.
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Eberhard Bänsch, Peter Benner, Jens Saak & Heiko K. Weichelt. (2015) Riccati-based Boundary Feedback Stabilization of Incompressible Navier--Stokes Flows. SIAM Journal on Scientific Computing 37:2, pages A832-A858.
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Ulrike Baur, Peter Benner & Lihong Feng. (2014) Model Order Reduction for Linear and Nonlinear Systems: A System-Theoretic Perspective. Archives of Computational Methods in Engineering 21:4, pages 331-358.
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Peter Benner & Patrick Kürschner. (2014) Computing real low-rank solutions of Sylvester equations by the factored ADI method. Computers & Mathematics with Applications 67:9, pages 1656-1672.
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Peter Benner & Tatjana Stykel. (2014) Numerical Solution of Projected Algebraic Riccati Equations. SIAM Journal on Numerical Analysis 52:2, pages 581-600.
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Peter Benner, Patrick Kürschner & Jens Saak. (2013) A Reformulated Low-Rank ADI Iteration with Explicit Residual Factors. PAMM 13:1, pages 585-586.
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Peter Benner & Jens Saak. (2013) Numerical solution of large and sparse continuous time algebraic matrix Riccati and Lyapunov equations: a state of the art survey. GAMM-Mitteilungen 36:1, pages 32-52.
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