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Peter Benner

Peter Benner - Publications

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Papers that can be retrieved from this page are either pdf files or postscript files compressed by gzip. If you have any problems downloading or uncompressing the files, please click here to request a hard copy.



Books

[B2]   [neu] 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 (in press).
[ISBN: 978-94-007-0088-8]
[B1]  Dimension Reduction of Large-Scale Systems
P. Benner, V. Mehrmann, and D.C. Sorensen (editors)
Lecture Notes in Computational Science and Engineering, Vol. 45, Springer-Verlag, Berlin/Heidelberg, June 2005.
[ISBN: 3-540-24545-6]

Submitted articles

[S14]  [new] L-Norm Computation for Continuous-Time Descriptor Systems Using Structured Matrix Pencils
Peter Benner, Vasile Sima, and Matthias Voigt
September 2010.
[S13]  [new] Krylov-Subspace Based Model Reduction of Nonlinear Circuit Models Using Bilinear and Quadratic-Linear Approximations
Peter Benner and Tobias Breiten
Submitted, September 2010.
[S12]  [new] Robust formulas for optimal H controllers
Peter Benner, Ralph Byers, Philip Losse, Volker Mehrmann, and Honnguo Xu
Preprint 20-2010, Preprint series of the Institute of Mathematics, Technische Universität Berlin, September 2010.
[S11]  [new] Accelerating Model Reduction of Large Linear Systems with Graphics Processors
Peter Benner, Pablo Ezzatti, Daniel Kressner, Enrique S. Quintana-Ortí, and Alfredo Remón
September 2010.
[S10] Krylov Subspace Methods for Model Order Reduction of Bilinear Discrete-Time Control Systems
Peter Benner, Tobias Breiten, and Tobias Damm
Submitted, May 2010.
[S9] Suboptimality Estimates for the Semi-Discretized LQR Problem for Parabolic PDEs
Peter Benner and Jens Saak
Submitted, May 2010.
[S8] Fast Model Reduction of Parametric Systems using Subspace Recycling
Lihong Feng, Peter Benner, and Jan G Korvink
Submitted, May 2010.
[S7] A structure-preserving algorithm for testing positive realness
Peter Benner, Delin Chu, and Xinmin Liu
Submitted, May 2010.
[S6] Efficient Balancing based MOR for Large Scale Second Order Systems
Peter Benner and Jens Saak
Submitted, March 2010.
[S5] 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.
[S4] 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.
[S3] 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
Research Report No. 2009-40, Seminar für Angewandte Mathematik, ETH Zürich, December 2009; revised August 2010.
[S2] Interpolatory Projection Methods for Parameterized Model Reduction
Ulrike Baur, Christopher Beattie, Peter Benner, and Serkan Gugercin
Chemnitz Scientific Computing Preprints 09-08, TU Chemnitz, November 2009.
[S1] Lyapunov Equations, Energy Functionals, and Model Order Reduction
Peter Benner and Tobias Damm
February 2009, revised March 2010.

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Refereed articles in journals

NOTE: The versions of the papers that can be downloaded from this page sometimes represent preliminary versions of the papers and not the final version published - unless the journal provides electronic versions of the papers. In the latter case, the links here are direct links to the versions provided by the journal.
In any case, we advise you to prefer the published articles as they contain the most recent versions.

[J70]  [new] Dimension Reduction for Damping Optimization in Linear Vibrating Systems
Peter Benner, Zoran Tomljanović, and Ninoslav Truhar
Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM), to appear.
Preliminary version appeared as Preprint 2/2010s, Department of Mathematics, J. J. Strossmayer University of Osijek, April 2010.
[J69]  [new] On the numerical solution of large-scale sparse discrete-time Riccati equations
Peter Benner and Heike Faßbender
Advances in Computational Mathematics, to appear.
Preliminary version appeared as Chemnitz Scientific Computing Preprints 09-11, TU Chemnitz, December 2009.
[J68]  [new]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, to appear.
[J67] A Hamiltonian Krylov-Schur-type method based on the symplectic Lanczos process
Peter Benner, Heike Faßbender, and Martin Stoll
Linear Algebra and Its Applications, to appear.
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.
[J66] 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 Preprints 09-04, TU Chemnitz, July 2009.
[J65] 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.
[J64] 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.
[J63] 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.
[J62] 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.
[J61] A Rational SHIRA Method for the Hamiltonian Eigenvalue Problem
Peter Benner and Cedric Effenberger
Taiwanese Journal of Mathematics, Vol. 14, No. 6A, pp. 805-823, 2010.
See also Chemnitz Scientific Computing Preprints 08-08, TU Chemnitz, December 2008.
[J60] 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.
[J59] 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.
[J58] 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.
[J57] Editorial: Large-Scale Matrix Equations of Special Type
Peter Benner.
Numerical Linear Algebra with Applications, Vol. 15, No. 9, pp. 747-754, 2008.
[J56] 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.
[J55] 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.
[J54] 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.
[J53] 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.
Partially extracted from [TR15].
[J52] 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.
Revised version of [TR13].
[J51] 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.
[J50] 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
[J49] 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
[J48]  Partial Realization of Descriptor Systems
Peter Benner and Viatcheslav I. Sokolov
Systems & Control Letters, Vol. 55, pp. 929-938, 2006.
[J47] 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.
[J46] 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.
[J45] 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
[J44]  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
[J43]  Numerical Linear Algebra for Model Reduction in Control and Simulation
Peter Benner
GAMM Mitteilungen, Vol. 29, No. 2, pp. 275-296, 2006.
See also Preprint 18/2005, Fakultät für Mathematik, TU Chemnitz.
[J42] 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, 2008.
Extended version of [CA42].
[J41] 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.
For the corresponding software visit the HAPACK homepage.
[J40] 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.
[J39] Balancing Sparse Hamiltonian Eigenproblems
Peter Benner and Daniel Kreßner
Linear Algebra and Its Applications, Vol. 415, pp. 3-19, 2006.
Original available from ScienceDirect, DOI: 10.1016/j.laa.2004.09.023
[J38] 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.
See also [CA19]
.
[J37] Solving Large-Scale Control Problems
Peter Benner
IEEE Control Systems Magazine, Vol. 24, No. 1, pp. 44-59, 2004.
[J36] 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.
The retrievable version appeared as Berichte aus der Technomathematik, Report 00-18, December 2000.
[J35] 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"), pp. 1701-1722, 2003.
[J34] Structure Preservation: A Challenge in Computational Control
Peter Benner, Daniel Kreßner, and Volker Mehrmann
Future Generation Computer Systems, Vol. 19, pp. 1243-1252, 2003.
[J33] On the Kleinman Iteration for Nonstabilizable Systems
Peter Benner, Vicente Hernández, and Antonio Pastor
Mathematics of Control, Signals, and Systems , Vol. 16, pp. 76-93, 2003.
The retrievable version appeared as Berichte aus der Technomathematik, Report 99-11, October 1999.
[J32] 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.
[J31] 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.
For an extended version, including detailed algorithms, see [TR10]
.
[J30] Efficient Algorithms for Large-Scale Quadratic Matrix Equations
Peter Benner
Proceedings in Applied Mathematics and Mechanics, Vol. 1, No. 1, pp. 492-495, 2002.
[J29] 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, pp. 306-325, 2002.
The retrievable version appeared as Berichte aus der Technomathematik, Report 01-02, February 2001.
[J28] 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.
[J27] 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.
The retrievable version appeared as Berichte aus der Technomathematik, Report 00-01, January 2000.
[J26] 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.
[J25] Computing Roots of Matrix Products
Peter Benner and Heike Faßbender
Zeitschrift für angewandte Mathematik und Mechanik, Vol. 81, Suppl. 2, pp. S717-S718, 2001.
[J24] On a Numerical Method for Regularization of Descriptor Systems
Peter Benner
Zeitschrift für angewandte Mathematik und Mechanik, Vol. 81, Suppl. 2, pp. S707-S708, 2001.
[J23] Cholesky-like Factorizations of Skew-Symmetric Matrices
Peter Benner, Ralph Byers, Heike Faßbender, Volker Mehrmann, and David 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.
[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.
The retrievable version appeared as Mathematics Research Reports 99-12-01, Department of Mathematics, University of Kansas, December 1999.
[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.
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, 2000.
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.
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.
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.
The retrievable 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, Vicente Hernández, and Enrique S. Quintana-Ortí
The Journal of Supercomputing, Vol. 15, pp. 193-206, 2000.
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, Josè M. Claver, and Enrique S. Quintana-Ortí
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 Watkins
Linear Algebra and its Applications, Vol. 287, pp. 41-76, 1999.
[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. 499-539, 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.
[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.
[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 Daivd Watkins
Linear Algebra and its Applications, Vol. 272, pp. 17-32, 1997.
[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, pp. 17-43, 1997.
[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. 7, No. 5, pp. 18-28, 1997.
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.
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.

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Book chapters

[BC10]  [new] 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, S. Ulbrich (editors), Constrained Optimization and Optimal Control for Partial Differential Equations, Birkhäuser, Basel, to appear.
[BC9]  [new]
      align= Partial Stabilization of Descriptor Systems Using Spectral Projectors
Peter Benner
In S. Bhattacharyya, R. Chan, P. Van Dooren, V. Olshevsky, A. Routray (editors), Numerical Linear Algebra in Signals, Systems and Control, Lecture Notes in Electrical Engineering, Springer-Verlag, to appear.
[BC8]  Control Theory
Peter Benner
In Leslie Hogben (editor), 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 (editors), 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]
[BC6] Model Reduction Based on Spectral Projection Methods
Peter Benner and Enrique S. Quintana-Ortí
In P. Benner, V. Mehrmann, and D.C. Sorensen (editors), Dimension Reduction of Large-Scale Systems, Ch. 1, Lecture Notes in Computational Science and Engineering, Springer-Verlag, Berlin/Heidelberg, June 2005.
[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 (editors), Dimension Reduction of Large-Scale Systems, Ch. 19, Lecture Notes in Computational Science and Engineering, Springer-Verlag, Berlin/Heidelberg, June 2005.
[BC4] Skew-Hamiltonian and Hamiltonian Eigenvalue Problems: Theory, Algorithms and Applications
Peter Benner, Daniel Kreßner, and Volker Mehrmann
In Z. Drmac, M. Marusic, and Z. Tutek (editors), Proceedings of the Conference on Applied Mathematics and Scientific Computing, pp. 3-39. Springer-Verlag, 2005.
[ISBN: 1-4020-3196-3]
Retrievable version is Preprint #2, DFG Research Center "Mathematics for Key Technologies", Berlin, November 2003.
[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 (editors), 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 (editors), Workshop on Wide Area Networks and High Performance Computing, Essen (Germany), September 1998, Lecture Notes in Control and Information, Vol. 249, pp. 61-88, Springer-Verlag, Berlin/Heidelberg, 1999. [ISBN 1-85233-642-0]
The retrievable version is NICONET Report 1999-1, Working Group on Software, January 1999.
[BC1] Numerical Methods for Linear Quadratic and $H_\infty$ Control Problems
Peter Benner, Ralp Byers, Volker Mehrmann, and Hongguo Xu
In G. Picci and D.S. Gilliam (editors), Dynamical Systems, Control, Coding, Computer Vision: New Trends, Interfaces, and Interplay, volume 25 of Progress in Systems and Control Theory, pp. 203-222, Birkhäuser, Basel, 1999. [ISBN: 3-7643-6060-7]

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Articles in conference proceedings

[CA85]  [new] On Stability, Passivity and Reciprocity Preservation of ESVDMOR
Peter Benner and André Schneider
In Peter Benner, Michael Hinze, E. Jan W. ter Maten (Eds.) Model Reduction for Circuit Simulation, Lecture Notes in Electrical Engineering, Vol. 74, Springer-Verlag, 2011 (in press). [ISBN: 978-94-007-0088-8]
[CA84]  [new] On Recycling Krylov Subspaces for Solving Linear Systems with Successive Right-Hand Sides with Applications in Model Reduction
Peter Benner and Lihong Feng
In Peter Benner, Michael Hinze, E. Jan W. ter Maten (Eds.) Model Reduction for Circuit Simulation, Lecture Notes in Electrical Engineering, Vol. 74, Springer-Verlag, 2011 (in press). [ISBN: 978-94-007-0088-8]
[CA83]  [new] Balanced Truncation Model Order Reduction for LTI Systems with many Inputs or Outputs
Peter Benner and André Schneider
In András Edelmayer (Ed.) Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2010), 5-9 July, 2010, Budapest, Hungary, pp. 1971-1974, 2010. [ISBN: 978-963-311-370-7]
[CA82]  [new] Numerical Solution of Differential Riccati Equations on Hybrid CPU-GPU Platforms
Peter Benner, Pablo Ezzatti, Hermann Mena, Enrique S. Quintana-Ortí, and Alfredo Remón
In Proceedings of ALAMA2010 - 2nd Meeting on Linear Algebra, Matrix Analysis, and Applications, Valencia, June 2nd-4th, 2010, 7 pages, 2010. [ISBN: 978-84-8363-544-5]
[CA81] H Control for Descriptor Systems - a Pencil Based Approach
Peter Benner and Philip Losse
Proceedings in Applied Mathematics and Mechanics, Vol. 9, pp. 645-646, 2009.
DOI: 10.1002/pamm.200910292.
[CA80] Computing the Eigenvalues of Hierarchical Matrices by LR-Cholesky Transformations
Peter Benner and Thomas Mach
Mathematisches Forschungsinstitut Oberwolfach, Report No. 37/2009, pp. 325-328, 2009.
DOI: 10.4171/OWR/2009/37.
[CA79] Model Reduction of Periodic Descriptor Systems Using Balanced Truncation
Peter Benner, Mohammad-Sahadet Hossain, and Tatjana Stykel
In Peter Benner, Michael Hinze, E. Jan W. ter Maten (Eds.) Model Reduction for Circuit Simulation, Lecture Notes in Electrical Engineering, Vol. 74, Springer-Verlag, 2011 (in press). (This version: July 2009).
[CA78] Novel Model Reduction Techniques for Control of Machine Tools
Peter Benner, Thomas Bonin, Heike Faßbender, Jens Saak, Andreas Soppa, and Michael Zaeh
In Proceedings of the ANSYS Conference & 27. CADFEM Users' Meeting 2009, 18.-20. November 2009, Congress Center Leipzig, paper 2.9.18 (10 pages), 2009.
[CA77] Using Hybrid CPU-GPU Platforms to Accelerate the Computation of the Matrix Sign Function
Peter Benner, Pablo Ezzatti, Enrique S. Quintana-Ortí, and Alfredo Remón
 [new] align=In H.-X. Lin, M. Alexander, M. Forsell, A. Knüpfer, R. Prodan, L. Sousa, and A. Streit (Eds.) Euro-Par 2009, Parallel Processing - Workshops., Lecture Notes in Computer Science, Vol. 6043, pp. 132-139, Springer-Verlag, Berlin/Heidelberg, 2010.
[CA76] Model Predictive Control for Nonlinear Parabolic Differential Equations Based on a Linear Quadratic Gaussian Design
Peter Benner and Sabine Hein
Proceedings in Applied Mathematics and Mechanics, Vol. 9, pp. 613-614, 2009.
DOI: 10.1002/pamm.200910278.
[CA75] Parametric Model Order Reduction Accelerated by Subspace Recycling
Lihong Feng, Peter Benner, and Jan G. Korvink
In Proceedings of 48th IEEE Conference on Decision and 28th Chinese Control Conference, Shanghai, P.R. China, December 16-18, 2009, pp. 4328-4333, 2009.
[CA74] System-Theoretic Methods for Model Reduction of Large-Scale Systems: Simulation, Control, and Inverse Problems
Peter Benner
In I. Troch and F. Breitenecker (Eds.), Proceedings of MathMod 2009, Vienna, February 11-13, 2009, ARGESIM Report no. 35, pp. 126-145, 2009. [ISBN: 978-3-901608-35-3]
[CA73] Efficient Balancing based MOR for Second Order Systems Arising in Control of Machine Tools
Peter Benner and Jens Saak
In I. Troch and F. Breitenecker (Eds.), Proceedings of MathMod 2009, Vienna, February 11-13, 2009, ARGESIM Report no. 35, 2009. [ISBN: 978-3-901608-35-3]
[CA72] Advances in Balancing-Related Model Reduction for Circuit Simulation
Peter Benner
In J. Roos and L.R.J. Costa (Eds.), Scientific Computing in Electrical Engineering SCEE 2008, Mathematics in Industry, Vol. 14, pp. 469-482, Springer-Verlag, Berlin/Heidelberg, 2010.
DOI: 10.1007/978-3-642-12294-1_58.
[CA71] Model Order and Terminal Reduction Approaches via Matrix Decomposition and Low Rank Approximation
Peter Benner and André Schneider
In J. Roos and L.R.J. Costa (Eds.), Scientific Computing in Electrical Engineering SCEE 2008, Mathematics in Industry, Vol. 14, pp. 523-530, Springer-Verlag, Berlin/Heidelberg, 2010.
DOI: 10.1007/978-3-642-12294-1_64.
[CA70] Model Order Reduction for Systems with Non-Rational Transfer Function Arising in Computational Electromagnetics
Lihong Feng and Peter Benner
In J. Roos and L.R.J. Costa (Eds.), Scientific Computing in Electrical Engineering SCEE 2008, Mathematics in Industry, Vol. 14, pp. 515-522, Springer-Verlag, Berlin/Heidelberg, 2010.
DOI: 10.1007/978-3-642-12294-1_63.
[CA69] Efficient Solution of Large Scale Lyapunov and Riccati Equations Arising in Model Order Reduction Problems
Jens Saak and Peter Benner
Proceedings in Applied Mathematics and Mechanics, Vol. 8, No. 1, pp. 10085-10088, 2008.
DOI: 10.1002/pamm.200810085
[CA68] Projection-Based Model Reduction for LTV Descriptor System Using Multipoint Krylov-Subspace Projectors
Mohammad-Sahadet Hossain and Peter Benner
Proceedings in Applied Mathematics and Mechanics, Vol. 8, No. 1, pp. 10081-10084, 2008.
DOI: 10.1002/pamm.200810081
[CA67] Flow Stabilisation by Dirichlet Boundary Control
René Schneider, Tobias Rothaug, and Peter Benner
Proceedings in Applied Mathematics and Mechanics, Vol. 8, No. 1, pp. 10961-10962, 2008.
DOI: 10.1002/pamm.200810961
[CA66] Parametrische Parametric Model Reduction with Sparse Grids
Ulrike Baur and Peter Benner
In B. Lohmann and A. Kugi (Eds.), Tagungsband GMA-FA 1.30 "Modellbildung, Identifizierung und Simulation in der Automatisierungstechnik", Workshop in Anif, 24.-26.9.2008, pp. 262-271, 2008. [ISBN: 978-3-9502451-3-4]
[CA65] Numerical Solution of Differential Riccati Equations Arising in Optimal Control for Parabolic PDEs
Hermann Mena and Peter Benner
Proceedings in Applied Mathematics and Mechanics, Vol. 7, No. 1, pp. 2060063-2060064, 2008.
DOI: 10.1002/pamm.200700913
[CA64] A Robust Algorithm for Parametric Model Order Reduction
Lihong Feng and Peter Benner
Proceedings in Applied Mathematics and Mechanics, Vol. 7, No. 1, pp. 1021501-1021502, 2008.
DOI: 10.1002/pamm.200700749
[CA63] Efficient Solution of Algebraic Bernoulli Equations Using H-Matrix Arithmetic
Ulrike Baur and Peter Benner
In K. Kunisch, G. Of, O. Steinbach (Eds.), Numerical Mathematics and Advanced Applications. Proceedings of ENUMATH 2007, the 7th European Conference on Numerical Mathematics and Advanced Applications, Graz, Austria, September 2007, pp. 127-134, Springer-Verlag, Heidelberg, 2008. [ISBN: 978-3-540-69776-3]
[CA62] Application of LQR Techniques to the Adaptive Control of Quasilinear Parabolic PDEs
Jens Saak and Peter Benner
Proceedings in Applied Mathematics and Mechanics, Vol. 7, No. 1, pp. 2060013-2060014, 2008.
DOI: 10.1002/pamm.200700240
[CA61] Parallel Implementation of LQG Balanced Truncation for Large-Scale Systems
José M. Badía, Peter Benner, Rafael Mayo, Enrique S. Quintana-Ortí, Gregorio Quintana-Ortí, and Alfredo Remón
In I. Lirkov, S. Margenov, J. Waniewski (Eds.), Large-Scale Scientific Computing. 6th International Conference, LSSC 2007, Sozopol, Bulgaria, June 5-9, 2007, Revised Papers, Lecture Notes in Computer Science, Vol. 4818, pp. 227-234, Springer-Verlag, Berlin, Heidelberg, New York, 2008. [ISBN: 978-3-540-78825-6]
[CA60] γ-Iteration for Descriptor Systems Using Structured Matrix Pencils
Peter Benner, Philip Losse, Volker Mehrmann, Lisa Poppe, and Timo Reis
In Proceedings of the 18th International Symposium on Mathematical Theory of Networks and Systems (MTNS2008), Virginia Tech, Blacksburg, Virginia, USA, July 28-August 1, 2008 (CD Rom), 11 pages, 2008.
[CA59] Using the Superposition Property for Model Reduction of Linear Systems with a Large Number of Inputs
Peter Benner, Lihong Feng, and Evgenii B. Rudnyi
In Proceedings of the 18th International Symposium on Mathematical Theory of Networks and Systems (MTNS2008), Virginia Tech, Blacksburg, Virginia, USA, July 28-August 1, 2008 (CD Rom), 12 pages, 2008.
[CA58] Experimental evaluation of new SLICOT solvers for linear matrix equations based on the matrix sign function
Vasile Sima and Peter Benner
In Proceedings of 2008 IEEE Multi-conference on Systems and Control. 9th IEEE International Symposium on Computer-Aided Control Systems Design (CACSD), Hilton Palacio del Rio Hotel, San Antonio, Texas, U.S.A., September 3-5, 2008, S. 601-606, Omnipress, Madison, WI, 2008. [ISBN: 978-1-4244-2223-4]
[CA57] Strategies for Parallelizing the Solution of Rational Matrix Equations
José M. Badía, Peter Benner, Maribel Castillo, Heike Faßbender, Rafael Mayo, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí
In C. Bischof, M. Bücker, P. Gibbon, G.R. Joubert, T. Lippert, B. Mohr, and F. Peters (editors), Parallel Computing: Architectures, Algorithms and Applications. Proceedings of the International Conference ParCo 2007, NIC Series Volume 38, pp. 255-262, John von Neumann-Institut für Computing, Jülich, Germany, 2007. [ISBN: 978-3-9810843-4-4]
[CA56] Parametrische Modellreduktion durch impliziten Momentenabgleich (Parametric Model Reduction by Implicit Moment Matching) [German]
Lihong Feng and Peter Benner
In B. Lohmann and A. Kugi (eds.), Tagungsband GMA-FA 1.30 "Modellbildung, Identifizierung und Simulation in der Automatisierungstechnik", Workshop in Anif, 26.-28.9.2007, pp. 34-47, 2007. [ISBN: 978-3-9502451-1-0]
[CA55] A Note on Projection Techniques for Model Order Reduction of Bilinear Systems
Lihong Feng and Peter Benner
In Theodore E. Simos, George Psihoyios, and Ch. Tsitouras (editors), Numerical Analysis and Applied Mathematics, International Conference of Numerical Analysis and Applied Mathematics. Corfu, September 16-21, 2007, AIP Conference Proceedings Vol. 936, pp. 208-211, Springer-Verlag, 2007. [ISBN: 978-0-7354-0447-2]
[CA54] Fast System Identification and Model Reduction Solvers
Vasile Sima and Peter Benner
In B.R. Andrievsky and A.L. Fradkov (editors), Preprints 9th IFAC Workshop ``Adaptation and Learning in Control and Signal Processing'' (ALCOSP 2007)}, August, 29-31, 2007, Saint Petersburg, Russia, IFAC-PapersOnline/Elsevier, 6 pages, 2007.
Retrieve local copy.
[CA53] MPC für nichtlineare partielle Differentialgleichungen parabolischen Typs (MPC for nonlinear partial differential equations of parabolic type) [German]
Peter Benner and Sabine Görner
In Tagungsband GMA-FA 1.40 "Theoretische Verfahren der Regelungstheorie" und GAMM-FA "Dynamik und Regelungstheorie", Workshops am Bostalsee, 24.-27.9.2006, pp. 91-101, 2006. [ISBN: 978-3-9810664-2-5]
[CA52] MPC for the Burgers Equation Based on an LQG Design
Peter Benner and Sabine Görner
Proceedings in Applied Mathematics and Mechanics, Vol. 6, No. 1, pp. 781-782, 2006.
DOI: 10.1002/pamm.200610371
[CA51]  Passivity Preserving Model Reduction via a Structured Lanczos Method
Peter Benner and Heike Faßbender
Proceedings of the 2006 IEEE Conference on Computer-Aided Control Systems Design, Munich, Germany, October 4-6, 2006, pp. 8-13, IEEE 2006.
[ISBN: 0-7803-9797-5]
[CA50]  A MATLAB Repository for Model Reduction Based on Spectral Projection
Peter Benner
Proceedings of the 2006 IEEE Conference on Computer-Aided Control Systems Design, Munich, Germany, October 4-6, 2006, pp. 19-24, IEEE 2006.
[ISBN: 0-7803-9797-5]
The corresponding software is (partially) available here.
[CA49] Parallel Solution of Large-Scale and Sparse Generalized Algebraic Riccati Equations
José M. Badía, Peter Benner, Rafael Mayo and Enrique S. Quintana-Ortí
In W. E. Nagel, W. V. Walter, and W. Lehner (editors): Euro-Par 2006 Parallel Processing: 12th International Euro-Par Conference, Lecture Notes in Computer Science, Vol. 4128, pp. 710-719. Springer-Verlag, Berlin, Heidelberg, New York, 2006.
DOI: 10.1007/11823285_74
[CA48]  A Numerical Algorithm for Robust Stabilization of Systems with Sector-Bounded Nonlinearity
Peter Benner
Preprints of the 5th IFAC Symposium on Robust Control Design, ROCOND'06, Toulouse, France, July 5-7, 2006.
[CA47]  A SLICOT Implementation of a Modified Newton's Method for Algebraic Riccati Equations
Vasile Sima and Peter Benner
Proceedings of the 14th Mediterranean Conference on Control and Automation MED06, June 28-30, 2006, Ancona - Università Politecnica delle Marche, Italy (CD-ROM) (6 pages).
[ISBN: 0-9786720-0-3]
[CA46] Parallel Algorithms for Balanced Truncation of Large-Scale Unstable Systems
Sergio Barrachina, Peter Benner, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí
In Proceedings of 44th IEEE Conference on Decision and European Control Conference ECC 2005, pp. 2248-2253, 2005. [ISBN: 0-7803-9568-9]
[CA45] New Hamiltonian Eigensolvers with Applications in Control
Peter Benner and Daniel Kreßner
In Proceedings of 44th IEEE Conference on Decision and European Control Conference ECC 2005, pp. 6551-6556, 2005. [ISBN: 0-7803-9568-9]
See also: Preprint #240, DFG Research Center MATHEON, Berlin, March 2005.
[CA44] Passivitätserhaltende Modellreduktion mit Balancierungstechniken (in German)
Peter Benner
In Tagungsband GMA-FA 1.30 "Modellbildung, Identifikation und Simulation in der Automatisierungstechnik", Workshop am Bostalsee, 28.-30.9.2005, pp. 152-168, 2005. [ISBN: 3-9810664-1-3]
[CA43] Parallel Order Reduction via Balanced Truncation for Optimal Cooling of Steel Profiles
José M. Badía, Peter Benner, Rafael Mayo, Enrique S. Quintana-Ortí Gregorio Quintana-Ortí, and Jens Saak
In J.C. Cunha, P.D. Mdeiros (eds.), Euro-Par 2005 Parallel Processing: 11th International Euro-Par Conference, Lisbon, Portugal, August 30 - September 2, 2005, Lecture Notes in Computer Science, Vol. 3648, pp. 857-866, Springer-Verlag, Berlin, Heidelberg, New York, 2005.
See also: Preprint SFB393/05-02, Sonderforschungsbereich 393 - Numerische Simulation auf massiv parallelen Rechnern, TU Chemnitz, January 2005.
[CA42] Parallel Solution of Large-Scale Algebraic Bernoulli Equations with the Matrix Sign Function Method
Sergio Barrachina, Peter Benner, and Enrique S. Quintana-Ortí
In T. Skeie, C.-S. Yang (editors), Proceedings of the 2005 International Conference on Parallel Processing Workshops, 14-17 June 2005, Oslo, Norway), pp. 189-193, IEEE Computer Society Press, 2005. [ISBN: 0-7695-2381-1]
[CA41] A New Test for Passivity of Descriptor Systems
Peter Benner and Delin Chu
Oberwolfach Reports, Vol. 2, No. 1, pp. 571-574, 2005.
[CA40] Efficient numerical solution of the LQR-problem for the heat equation
Peter Benner and Jens Saak
Proceedings in Applied Mathematics and Mechanics, Vol. 4, No. 1, pp. 648-649, 2004.
[CA39] Parallel Algorithms for Balanced Truncation Model Reduction of Sparse Systems
José Manuel Badía, Peter Benner, Rafael Mayo, and Enrique S. Quintana-Ortí
In J. Dongarra, K. Madsen, J. Wasniewski (editors),Applied Parallel Computing: 7th International Conference, PARA 2004, Lyngby, Denmark, June 20-23, 2004. Revised Selected Papers, Lecture Notes in Computer Science, Springer-Verlag, Vol. 3732, pp. 267-275, 2006. [ISBN: 3-540-29067-4]
Original available from SpringerLink, DOI: 10.1007/11558958_32
[CA38] Factorized solution of the Lyapunov equation by using the hierarchical matrix arithmetic
Ulrike Baur and Peter Benner
Proceedings in Applied Mathematics and Mechanics, Vol. 4, No. 1, pp. 658-659, 2004.
[CA37] A Robust Numerical Method for Optimal H_inf Control
Peter Benner, Ralph Byers, Volker Mehrmann, and Hongguo Xu
Proceedings 43rd IEEE Conference on Decision and Control CDC2004, pp. 424-425, Omnipress, Madison, WI, 2004. [ISBN: 0-7803-8683-3]
Very short version of [TR13].
[CA36] Computing Optimal Hankel Norm Approximations of Large-Scale Systems
Peter Benner, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí
Proceedings of 43rd IEEE Conference on Decision and Control CDC2004, pp. 3078-3083, Omnipress, Madison, WI, 2004. [ISBN: 0-7803-8683-3]
The retrievable version is Preprint #116, DFG Research Center "Mathematics for Key Technologies", Berlin, April 2004.
[CA35] Computing Passive Reduced-Order Models for Circuit Simulation
Peter Benner, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí
In Proceedings International Conference on Parallel Computing in Electrical Engeneering PARELEC 2004, pp. 146-151, IEEE Computer Society, Los Alamitos, CA, 2004.
[ISBN: 0-7695-2080-4]
[CA34] Factorized Solution of Sylvester Equations with Applications in Control
Peter Benner
In B. De Moor, B. Motmans, J. Willems, P. Van Dooren, V. Blondel (editors), Proceedings Sixteenth International Symposium on: Mathematical Theory of Network and Systems, MTNS 2004, Leuven, Belgium, July 5-9, 2004.
[CA33] BDF Methods for Large-Scale Differential Riccati Equations
Peter Benner and Hermann Mena
In B. De Moor, B. Motmans, J. Willems, P. Van Dooren, V. Blondel (editors), Proceedings Sixteenth International Symposium on: Mathematical Theory of Network and Systems, MTNS 2004, Leuven, Belgium, July 5-9, 2004.
[CA32] Parallel Model Reduction of Large-Scale Linear Descriptor Systems via Balanced Truncation
Peter Benner, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí
In M. Daydé, J.J. Dongarra, V. Hernández, J.M.L.M. Palma (editors), High Performance Computing for Computational Science - VECPAR 2004, Lecture Notes in Computer Science, No. 3402, pp. 340-353, Springer-Verlag, Berlin/Heidelberg 2005. [ISBN: 3-540-25424-2]
[CA31] A Structure-Preserving Method for Generalized Algebraic Riccati Equations Based on Pencil Arithmetic
Ralph Byers and Peter Benner
Proceedings of the European Control Conference ECC'03, September 1-4, 2003, Cambridge, UK. (CD Rom).
[CA30] Solving Linear Matrix Equations with SLICOT
Vasile Sima and Peter Benner
Proceedings of the European Control Conference ECC'03, September 1-4, 2003, Cambridge, UK. (CD Rom).
[CA29] Parallel Model Reduction of Large-Scale Unstable Systems
Peter Benner, Maribel Castillo, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí
In G.R. Joubert, W.E. Nagel, F.J. Peters, W.V Walter (editors), Parallel computing: Software Technology, Algorithms, Architectures & Applications, Advances in Parallel Computing, Vol. 13, pp. 251-258, Elsevier B.V (North-Holland), 2004.
[ISBN: 0-444-51689-1]
[CA28] Solving Algebraic Riccati Equations with SLICOT

Peter Benner and Vasile Sima
Proceedings of the 11th Mediterranean Conference on Control & Automation MED'03, June 18-20, 2003, Rhodes (CD Rom), paper IV01-1 (6 pages), 2003.
[CA27] A Service for Remote Model Reduction of Very Large Linear Systems
Peter Benner, Rafael Mayo, Enrique S. Quintana-Ortí and Gregorio Quintana-Ortí
In Proceedings of 17th International Parallel & Distributed Processing Symposium (IPDPS 2003), paper W16-PDSECA-22, 6 pages. IEEE Computer Society Press, 2003. [ISBN: 0-7695-1926-1]
[CA26] Partial Stabilization of Generalized State-Space Systems Using the Disk Function Method
Peter Benner
Proceedings in Applied Mathematics and Mechanics, Vol. 2, No. 1, pp. 479-480, 2003.
[CA25] Solving Large Sparse Lyapunov Equations on Parallel Computers
José Manuel Badía, Peter Benner, Rafael Mayo, and Enrique S. Quintana-Ortí
In B. Monien, R. Feldmann (editors), Euro-Par 2002 Parallel Processing, Lecture Notes in Computer Science, No. 2400, pp. 687-690, Springer-Verlag, 2002.
[ISBN: 3-540-44049-6]
[CA24] A Sparse Approximate Inverse Preconditioner for the Method of Moments Accelerated with the Multilevel Fast Multipole Method
Peter Benner, Martin Brüning, Angelika Bunse-Gerstner, Rainer Bunger, Jan M. Reiter, and Jan Ritter
Proceedings of 2002 IEEE Intl. Symp. on Antennas & Propagation and USN/URSI Meeting, June 16-21, 2002, San Antonio, Texas, pp. 602-605.
[CA23] A Web Service for Model Reduction of Large-Scale Linear Systems on a Cluster

José Manuel Badía, Peter Benner, Maribel Castillo, Rafael Mayo, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí
Proceedings of XIII Jornadas de Paralelismo, Lérida (Spain), pp. 383-388, 2002.
[ISBN: 84-8409-159-7]
[CA22] Remote Parallel Model Reduction of Linear Time-Invariant Systems Made Easy
Peter Benner, Rafael Mayo, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí
In J.M.L.M. Palma, V. Hernández, J.J. Dongarra, and A.A. Sousa (editors), High Performance Computing for Computational Science - VECPAR 2002, Lecture Notes in Computer Science, Springer-Verlag, No. 2565, pp. 255-268, 2003. [ISBN: 3-540-00852-7]
Version in on-site conference proceedings:
A Mail Service for Parallel Model Reduction of Linear Time-Invariant Systems
Proceedings of VECPAR'02, 5th Intl. Meeting on High-Performance Computing for Computational Science, Porto, Portugal, June 26-28, 2002, pp. 735-746.
[CA21] Enhanced services for remote model reduction of large-scale dense linear systems
Peter Benner, Rafael Mayo, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí
In J. Fagerholm, J. Haataja, J. Järvinen, M. Lyly, P. Raback, and V. Savolainen (editors), Applied Parallel Computing. PARA'02 6th International Conference, Espoo (Finland), 2002, Lecture Notes in Computer Science, No. 2367, pp. 329-338, Springer-Verlag, 2002. [ISBN: 3-540-43786-X]
[CA20] A Coarse-Grain Parallel Solver for Riccati Equations
Peter Benner, Rafael Mayo, Enrique S. Quintana-Ortí, and Vicente Hernández
In G.R. Joubert, A. Murli, F.J. Peters, M. Vanesschi (Eds.), Parallel Computing. Advances and Current Issues. Proceedings of the International Conference ParCo2001, pp. 274-281, Imperial College Press, London, UK, 2002. [ISBN: 1-86094-315-2]
[CA19] Partial Stabilization of Large-Scale Discrete-Time Linear Control Systems
Peter Benner, Maribel Castillo, and Enrique S. Quintana-Ortí
Proceedings of the 2001 ICPP Workshops (Workshop on High Performance Scientific and Engineering Computing with Applications), Valencia, September 3-7, 2001, pp. 93-98, IEEE Computer Society Press, Los Alamitos, CA, 2001. [ISBN: 0-7695-1260-7]
[CA18] PSLICOT Routines for Model Reduction of Stable Large-Scale Systems
Peter Benner, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí
Proceedings of the Third NICONET Workshop on Numerical Software in Control Engineering, Louvain-la-Neuve, Belgium, January 19, 2001, pp. 39-44.
[CA17] Model Reduction of Large-Scale Dense Systems
Peter Benner, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí
Proceedings of the IEE UKACC International Conference CONTROL 2000, Cambridge, UK, 4-7 September 2000, IEE ZZ057 (CD Rom), 2000. [ISBN: 0-85296-240-1]
[CA16] Singular Perturbation Approximation of Large, Dense Linear Systems
Peter Benner, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí
Proceedings of the 2000 IEEE International Symposium on Computer Aided Control System Design, Anchorage, Alaska, USA, September 25-27, 2000, pp. 255-260. Omnipress, Madison, WI, 2000.
[CA15] Solving Discrete-Time Periodic Riccati Equations on a Cluster

Peter Benner, Rafael Mayo, Enrique S. Quintana-Ortí and Vicente Hernández
In A. Bode, T. Ludwig, W. Karl, and R. Wismüller (editors), Euro-Par 2000 Parallel Processing, Lecture Notes in Computer Science, No. 1900, pp. 824-828, Springer-Verlag, 2000. [ISBN: 3-540-67956-1]
[CA14] Efficient Numerical Model Reduction Methods for Discrete-Time Systems
Peter Benner, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí
In I. Troch, F. Breitenecker (editors), Proceedings of the IMACS Symposium on Mathematical Modelling, 3rd MATHMOD Vienna, Vienna University of Technology, Austria, February 2-4, 2000, Vol. 1, pp. 277-280, ARGESIM Reports No. 15. [ISBN: 3-901608-15-X]
[CA13] An Arithmetic for Rectangular Matrix Pencils

Peter Benner and Ralp Byers
In O. Gonzalez (editor), Proceedings of the 1999 IEEE International Symposium on Computer Aided Control System Design, Kohala Coast-Island of Hawai'i, Hawai'i, USA, August 22-27, 1999, pp. 75-80. [ISBN: 0-7803-5449-4]
[CA12] Numerical Solution of Linear-Quadratic Control Problems for Descriptor Systems
Peter Benner, Ralph Byers, Volker Mehrmann, and Hongguo Xu
In O. Gonzalez (editor), Proceedings of the 1999 IEEE International Symposium on Computer Aided Control System Design, Kohala Coast-Island of Hawai'i, Hawai'i, USA, August 22-27, 1999, pp. 64-69. [ISBN: 0-7803-5449-4]
[CA11] Solving Linear and Quadratic Matrix Equations on Distributed Memory Parallel Computers
Peter Benner, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí
In O. Gonzalez (editor), Proceedings of the 1999 IEEE International Symposium on Computer Aided Control System Design, Kohala Coast-Island of Hawai'i, Hawai'i, USA, August 22-27, 1999, pp. 46-51. [ISBN: 0-7803-5449-4]
[CA10] Initializing Newton's Method for Discrete-Time Algebraic Riccati Equations Using the Butterfly SZ Algorithm
Peter Benner and Heike Faßbender
In O. Gonzalez (editor), Proceedings of the 1999 IEEE International Symposium on Computer Aided Control System Design, Kohala Coast-Island of Hawai'i, Hawai'i, USA, August 22-27, 1999, pp. 70-74.
[ISBN: 0-7803-5449-4]
[CA9] Solving Stable Stein Equations on Distributed Memory Computers

Peter Benner, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí
In P. Amestoy, P. Berger, M. Daydé, I. Duff, V. Frayssé, L. Giraud and D. Ruiz (editors), EuroPar'99 Parallel Processing, Lecture Notes in Computer Science, No. 1685, Springer-Verlag, 1999, pp. 1120-1123. [ISBN 3-540-66443-2]
[CA8] Accelerating Newton's Method for Discrete-Time Algebraic Riccati Equations
Peter Benner
In A. Beghi, L. Finesso, and G. Picci (editors), Mathematical Theory of Networks and Systems. Proceedings of the MTNS-98 Symposium held in Padova, Italy, July, 1998, pp. 569-572, Il Poligrafo, Padova, 1998. [ISBN: 88-7115-117-8]
[CA7] An Arithmetic for Matrix Pencils

Peter Benner and Ralp Byers
In A. Beghi, L. Finesso, and G. Picci (editors), Mathematical Theory of Networks and Systems. Proceedings of the MTNS-98 Symposium held in Padova, Italy, July, 1998, pp. 573-576, Il Poligrafo, Padova, 1998. [ISBN: 88-7115-117-8]
[CA6] Improving the efficiency and accuracy of the MATLAB Control Toolbox using SLICOT-based gateways
Vasile Sima, Peter Benner, Sabine Van Huffel, and Andras Varga
In A. Beghi, L. Finesso, and G. Picci (editors), Mathematical Theory of Networks and Systems. Proceedings of the MTNS-98 Symposium held in Padova, Italy, July, 1998, pp. 673-676, Il Poligrafo, Padova, 1998. [ISBN: 88-7115-117-8]
[CA5] Efficient Solution of Coupled Lyapunov Equations via Matrix Sign Function Iteration.
Peter Benner, José M. Claver, and Enrique S. Quintana-Ortí
Proceedings of the 3rd Portuguese Conference on Automatic Control CONTROLO'98, Coimbra, September 9-11, 1998, pp. 205-210.
[CA4] Numerical Solution of Special Algebraic Riccati Equations via an Exact Line Search Method
Peter Benner
Proceedings of the European Control Conference ECC97 (CD-ROM), Paper 786, BELWARE Information Technology, Waterloo (B), 1997.
[CA3] A New Method for the Hamiltonian Eigenvalue Problem
Peter Benner, Volker Mehrmann, and Hongguo Xu
Proceedings of the European Control Conference ECC97 (CD-ROM), Paper 785, BELWARE Information Technology, Waterloo (B), 1997.
[CA2] Disk Functions and their Relationship to the Matrix Sign Function

Peter Benner and Ralph Byers
Proceedings of the European Control Conference ECC97 (CD-ROM), Paper 936, BELWARE Information Technology, Waterloo (B), 1997.
[CA1] Step Size Control for Newton's Method Applied to Algebraic Riccati Equations
Peter Benner and Ralph Byers
Proceedings of the Fifth SIAM Conference on Applied Linear Algebra, pp. 177-181, SIAM, Philadelphia, 1994.

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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).


[TR18] The SLICOT Toolboxes - a Survey
Peter Benner, Daniel Kressner, Vasile Sima, and Andras Varga
SLICOT Working Note 2009-1, August 2009.
[TR17] Modellordnungsreduktion für strukturmechanische FEM-Modelle von Werkzeugmaschinen [German]
Peter Benner
Project Report, Chemnitz University of Technology, May 2008.
[TR16] 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.
[TR15] 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.
[TR14] 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.
[TR13] 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.
[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.

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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 (ed.), 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.

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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.

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Other publications

[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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