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## Benner, Peter

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 Author ID: benner.peter Published as: Benner, Peter; Benner, P. Homepage: https://www.mpi-magdeburg.mpg.de/benner External Links: MGP · ORCID · Wikidata · Google Scholar · ResearchGate · dblp · GND
 Documents Indexed: 255 Publications since 1993, including 12 Books
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#### Co-Authors

 10 single-authored 23 Saak, Jens 21 Quintana-Ortí, Enrique S. 20 Feng, Lihong 18 Faßbender, Heike 14 Mehrmann, Volker 14 Stoll, Martin 12 Byers, Ralph 12 Quintana-Ortí, Gregorio 11 Grundel, Sara 10 Breiten, Tobias 10 Kürschner, Patrick 9 Baur, Ulrike 8 Goyal, Pawan 8 Kressner, Daniel 8 Xu, Hongguo 7 Stykel, Tatjana 7 Voigt, Matthias 7 Weichelt, Heiko K. 6 Mayo, Rafael 6 Mena, Hermann 6 Redmann, Martin 6 Rozza, Gianluigi 5 Banagaaya, Nicodemus 5 Heiland, Jan 5 Mach, Thomas 5 Yücel, Hamdullah 4 Damm, Tobias 4 Grivet-Talocia, Stefano 4 Gugercin, Serkan 4 Hess, Martin W. 4 Himpe, Christian 4 Hinze, Michael 4 Khoromskaia, Venera 4 Khoromskij, Boris N. 4 Onwunta, Akwum 4 Quarteroni, Alfio M. 4 Remón, Alfredo 4 Silveira, Luís Miguel 4 Trautwein, Christoph 4 Truhar, Ninoslav 3 Ahmad, Mian Ilyas 3 Badía, José M. 3 Bänsch, Eberhard 3 Bujanović, Zvonimir 3 Dolgov, Sergey V. 3 Ezzatti, Pablo 3 Hernández, Vicente G. 3 Hossain, Mohammad-Sahadet 3 Li, Suzhou 3 Meuris, Peter 3 Mitchell, Tim 3 Ohlberger, Mario 3 Schilders, Wil H. A. 3 Schneider, René 3 Schoenmaker, Wim 3 Sima, Vasile 3 Tischendorf, Caren 3 Watkins, David S. 3 Werner, Steffen W. R. 3 Willcox, Karen E. 3 Zhang, Yongjin 3 Zuyev, Aleksandr Leonidovich 2 Aliyev, Nicat 2 Antoulas, Athanasios C. 2 Castillo, Maribel 2 Clees, Tanja 2 Heinkenschloss, Matthias 2 Hornung, Nils 2 Korvink, Jan G. 2 Losse, Philip 2 Mengi, Emre 2 Patera, Anthony T. 2 Pontes Duff, Igor 2 Qiu, Yue 2 Rodriguez Cruz, Yolanda Rocio 2 Sadkane, Miloud 2 Schilders, Wilhelmus H. A. 2 Schneider, André 2 Seidel-Morgenstern, Andreas 2 Sorensen, Danny C. 2 Sundmacher, Kai 2 Tomljanović, Zoran 2 Uddin, Mohammad Monir 2 Urban, Karsten 2 Yue, Yao 2 Zimmermann, Ralf 1 Ahuja, Kapil 1 Ammar, Gregory S. 1 Asif, Mian Mohammad Arsalan 1 Baldin, Anton 1 Baran, Björn 1 Barrachina, Sergio 1 Barth, Eric 1 Baumann, Manuel 1 Beattie, Christopher A. 1 Behr, Maximilian 1 Binev, Daniel 1 Bollhöfer, Matthias 1 Börm, Steffen 1 Bosch, Jessica ...and 97 more Co-Authors
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#### Serials

 16 SIAM Journal on Scientific Computing 15 Linear Algebra and its Applications 10 ETNA. Electronic Transactions on Numerical Analysis 10 Advances in Computational Mathematics 9 SIAM Journal on Matrix Analysis and Applications 7 PAMM. Proceedings in Applied Mathematics and Mechanics 6 Journal of Computational and Applied Mathematics 6 Numerical Algorithms 6 Numerical Linear Algebra with Applications 6 Mathematical and Computer Modelling of Dynamical Systems 5 IEEE Transactions on Automatic Control 5 Systems & Control Letters 4 Numerische Mathematik 4 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 3 Journal of Computational Physics 3 MCSS. Mathematics of Control, Signals, and Systems 3 GAMM-Mitteilungen 2 Computers & Mathematics with Applications 2 Computer Methods in Applied Mechanics and Engineering 2 Journal of the Franklin Institute 2 ACM Transactions on Mathematical Software 2 BIT 2 Computing 2 International Journal for Numerical Methods in Engineering 2 SIAM Journal on Numerical Analysis 2 Parallel Computing 2 Applied Numerical Mathematics 2 Applied Mathematical Modelling 2 Computational Optimization and Applications 2 Journal of Numerical Mathematics 2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 2 ISNM. International Series of Numerical Mathematics 2 Numerical Algebra, Control and Optimization 2 SIAM/ASA Journal on Uncertainty Quantification 1 International Journal of Control 1 International Journal of Systems Science 1 Journal of Mathematical Analysis and Applications 1 Mitteilungen der Deutschen Mathematiker-Vereinigung (DMV) 1 Applied Mathematics and Computation 1 Automatica 1 Calcolo 1 Mathematische Nachrichten 1 SIAM Journal on Control and Optimization 1 COMPEL 1 Applied Mathematics Letters 1 Journal of Scientific Computing 1 Journal of Parallel and Distributed Computing 1 The Journal of Supercomputing 1 SIAM Review 1 International Journal of Robust and Nonlinear Control 1 Analele Ştiinţifice ale Universităţii “Ovidius” Constanţa. Seria: Matematică 1 Discrete and Continuous Dynamical Systems 1 Parallel Algorithms and Applications 1 Computing and Visualization in Science 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 Vietnam Journal of Mathematics 1 Optimization Methods & Software 1 Taiwanese Journal of Mathematics 1 International Journal of Applied Mathematics and Computer Science 1 Archives of Computational Methods in Engineering 1 Computational Methods in Applied Mathematics 1 Stochastics and Dynamics 1 Journal of Applied Mathematics and Computing 1 Lecture Notes in Computational Science and Engineering 1 Mathematics in Industry 1 Computational Science & Engineering 1 JNAIAM. Journal of Numerical Analysis, Industrial and Applied Mathematics 1 Networks and Heterogeneous Media 1 EURASIP Journal on Advances in Signal Processing 1 Applied and Computational Mathematics 1 Algorithms 1 MS&A. Modeling, Simulation and Applications 1 The Journal of Mathematical Neuroscience 1 Journal of Mathematics in Industry 1 Stochastic and Partial Differential Equations. Analysis and Computations 1 Journal of Computational Dynamics 1 Modeling and Simulation in Science, Engineering and Technology
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#### Fields

 167 Numerical analysis (65-XX) 117 Systems theory; control (93-XX) 67 Linear and multilinear algebra; matrix theory (15-XX) 30 Calculus of variations and optimal control; optimization (49-XX) 26 Partial differential equations (35-XX) 19 General and overarching topics; collections (00-XX) 18 Fluid mechanics (76-XX) 16 Ordinary differential equations (34-XX) 15 Optics, electromagnetic theory (78-XX) 10 Probability theory and stochastic processes (60-XX) 9 Dynamical systems and ergodic theory (37-XX) 8 Computer science (68-XX) 7 Mechanics of deformable solids (74-XX) 5 Classical thermodynamics, heat transfer (80-XX) 5 Statistical mechanics, structure of matter (82-XX) 4 Mechanics of particles and systems (70-XX) 4 Operations research, mathematical programming (90-XX) 4 Biology and other natural sciences (92-XX) 3 Approximations and expansions (41-XX) 3 Information and communication theory, circuits (94-XX) 2 History and biography (01-XX) 2 Geophysics (86-XX) 1 Combinatorics (05-XX) 1 Sequences, series, summability (40-XX) 1 Functional analysis (46-XX) 1 Operator theory (47-XX) 1 Geometry (51-XX) 1 Statistics (62-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)

#### Citations contained in zbMATH Open

195 Publications have been cited 2,088 times in 1,007 Documents Cited by Year
A survey of projection-based model reduction methods for parametric dynamical systems. Zbl 1339.37089
Benner, Peter; Gugercin, Serkan; Willcox, Karen
2015
Numerical solution of large-scale Lyapunov equations, Riccati equations, and linear-quadratic optimal control problems. Zbl 1212.65245
Benner, P.; Li, J.-R.; Penzl, T.
2008
Dimension reduction of large-scale systems. Proceedings of a workshop, Oberwolfach, Germany, October 19–25, 2003. Zbl 1066.65004
Benner, Peter (ed.); Mehrmann, Volker (ed.); Sorensen, Danny C. (ed.)
2005
Lyapunov equations, energy functionals, and model order reduction of bilinear and stochastic systems. Zbl 1217.93158
Benner, Peter; Damm, Tobias
2011
On the ADI method for Sylvester equations. Zbl 1176.65050
Benner, Peter; Li, Ren-Cang; Truhar, Ninoslav
2009
Model order reduction for linear and nonlinear systems: a system-theoretic perspective. Zbl 1348.93075
Baur, Ulrike; Benner, Peter; Feng, Lihong
2014
Numerical solution of large and sparse continuous time algebraic matrix Riccati and Lyapunov equations: a state of the art survey. Zbl 1279.65044
Benner, Peter; Saak, Jens
2013
Interpolatory projection methods for parameterized model reduction. Zbl 1254.93032
Baur, Ulrike; Beattie, Christopher; Benner, Peter; Gugercin, Serkan
2011
Interpolation-based $${\mathcal H}_2$$-model reduction of bilinear control systems. Zbl 1256.93027
Benner, Peter; Breiten, Tobias
2012
Solving stable generalized Lyapunov equations with the matrix sign function. Zbl 0940.65035
Benner, Peter; Quintana-Ortí, Enrique S.
1999
Model reduction and approximation. Theory and algorithms. Zbl 1378.65010
Benner, Peter (ed.); Cohen, Albert (ed.); Ohlberger, Mario (ed.); Willcox, Karen (ed.)
2017
A numerically stable, structure preserving method for computing the eigenvalues of real Hamiltonian or symplectic pencils. Zbl 0889.65036
Benner, Peter; Mehrmann, Volker; Xu, Hongguo
1998
Low rank methods for a class of generalized Lyapunov equations and related issues. Zbl 1266.65068
Benner, Peter; Breiten, Tobias
2013
An implicitly restarted symplectic Lanczos method for the Hamiltonian eigenvalue problem. Zbl 0884.65028
Benner, Peter; Faßbender, Heike
1997
Numerical computation of deflating subspaces of skew-Hamiltonian/Hamiltonian pencils. Zbl 1035.49022
Benner, Peter; Byers, Ralph; Mehrmann, Volker; Xu, Hongguo
2002
SLICOT – a subroutine library in systems and control theory. Zbl 1051.93500
Benner, Peter; Mehrmann, Volker; Sima, Vasile; Van Huffel, Sabine; Varga, Andras
1999
Factorized solution of Lyapunov equations based on hierarchical matrix arithmetic. Zbl 1111.65039
Baur, U.; Benner, P.
2006
Efficient handling of complex shift parameters in the low-rank Cholesky factor ADI method. Zbl 1267.65047
Benner, Peter; Kürschner, Patrick; Saak, Jens
2013
Self-generating and efficient shift parameters in ADI methods for large Lyapunov and Sylvester equations. Zbl 1312.65068
Benner, Peter; Kürschner, Patrick; Saak, Jens
2014
An exact line search method for solving generalized continuous-time algebraic Riccati equations. Zbl 0908.93026
Benner, Peter; Byers, Ralph
1998
Cross-Gramian based model reduction for data-sparse systems. Zbl 1170.93315
Baur, Ulrike; Benner, Peter
2008
Rosenbrock methods for solving Riccati differential equations. Zbl 1369.65088
Benner, Peter; Mena, Hermann
2013
An improved numerical method for balanced truncation for symmetric second-order systems. Zbl 1305.93043
Benner, Peter; Kürschner, Patrick; Saak, Jens
2013
A semi-discretized heat transfer model for optimal cooling of steel profiles. Zbl 1170.80341
Benner, Peter; Saak, Jens
2005
On the numerical solution of large-scale sparse discrete-time Riccati equations. Zbl 1230.65070
Benner, Peter; Faßbender, Heike
2011
Model reduction for stochastic systems. Zbl 1331.65017
Benner, Peter; Redmann, Martin
2015
A new method for computing the stable invariant subspace of a real Hamiltonian matrix. Zbl 1005.65034
Benner, Peter; Mehrmann, Volker; Xu, Hongguo
1997
Cholesky-like factorizations of skew-symmetric matrices. Zbl 0963.65033
Benner, Peter; Byers, Ralph; Fassbender, Heike; Mehrmann, Volker; Watkins, David
2000
Model order reduction for PDE constrained optimization. Zbl 1327.49043
Benner, Peter; Sachs, Ekkehard; Volkwein, Stefan
2014
A robust algorithm for parametric model order reduction based on implicit moment matching. Zbl 1312.65109
Benner, Peter; Feng, Lihong
2014
Numerical solution of the infinite-dimensional LQR problem and the associated Riccati differential equations. Zbl 1444.65032
Benner, Peter; Mena, Hermann
2018
A robust numerical method for the $$\gamma$$-iteration in $$H_{\infty}$$ control. Zbl 1124.93022
Benner, Peter; Byers, Ralph; Mehrmann, Volker; Xu, Hongguo
2007
Efficient balancing-based MOR for large-scale second-order systems. Zbl 1221.93039
Benner, Peter; Saak, Jens
2011
Model order reduction of differential algebraic equations arising from the simulation of gas transport networks. Zbl 1319.65077
Grundel, Sara; Jansen, Lennart; Hornung, Nils; Clees, Tanja; Tischendorf, Caren; Benner, Peter
2014
Evaluating products of matrix pencils and collapsing matrix products. Zbl 1055.65053
Benner, Peter; Byers, Ralph
2001
Two-sided projection methods for nonlinear model order reduction. Zbl 1312.93016
Benner, Peter; Breiten, Tobias
2015
Skew-Hamiltonian and Hamiltonian eigenvalue problems: theory, algorithms and applications. Zbl 1069.65034
Benner, Peter; Kressner, Daniel; Mehrmann, Volker
2005
Contributions to the numerical solution of algebraic Riccati equations and related eigenvalue problems. Zbl 0896.65047
Benner, Peter
1997
Model order reduction for differential-algebraic equations: a survey. Zbl 1402.93069
Benner, Peter; Stykel, Tatjana
2017
$$\mathcal H_2$$-quasi-optimal model order reduction for quadratic-bilinear control systems. Zbl 1418.93048
Benner, Peter; Goyal, Pawan; Gugercin, Serkan
2018
On the solution of large-scale algebraic Riccati equations by using low-dimensional invariant subspaces. Zbl 1330.15017
Benner, Peter; Bujanović, Zvonimir
2016
Efficient algorithms for generalized algebraic Bernoulli equations based on the matrix sign function. Zbl 1132.65033
Barrachina, Sergio; Benner, Peter; Quintana-Ortí, Enrique S.
2007
Balanced truncation model reduction of large-scale dense systems on parallel computers. Zbl 0978.93013
Benner, Peter; Quintana-Ortí, Enrique S.; Quintana-Ortí, Gregorio
2000
Perturbation analysis for the eigenvalue problem of a formal product of matrices. Zbl 1003.65032
Benner, Peter; Mehrmann, Volker; Xu, Hongguo
2002
Computing real low-rank solutions of Sylvester equations by the factored ADI method. Zbl 1364.65093
Benner, Peter; Kürschner, Patrick
2014
Generalised tangential interpolation for model reduction of discrete-time MIMO bilinear systems. Zbl 1230.93010
Benner, P.; Breiten, T.; Damm, T.
2011
An arithmetic for matrix pencils: theory and new algorithms. Zbl 1101.65046
Benner, Peter; Byers, Ralph
2006
The symplectic eigenvalue problem, the butterfly form, the SR algorithm, and the Lanczos method. Zbl 0935.65030
Benner, Peter; Faßbender, Heike
1998
Recycling BiCGSTAB with an application to parametric model order reduction. Zbl 1325.65044
Ahuja, Kapil; Benner, Peter; de Sturler, Eric; Feng, Lihong
2015
RADI: a low-rank ADI-type algorithm for large scale algebraic Riccati equations. Zbl 1385.65035
Benner, Peter; Bujanović, Zvonimir; Kürschner, Patrick; Saak, Jens
2018
Low-rank solvers for unsteady Stokes-Brinkman optimal control problem with random data. Zbl 1423.76329
Benner, Peter; Dolgov, Sergey; Onwunta, Akwum; Stoll, Martin
2016
Model reduction of parametrized systems. Selected contributions based on the presentations at the MoRePaS conference, SISSA, Trieste, Italy, October 13–16, 2015. Zbl 1381.65001
Benner, Peter (ed.); Ohlberger, Mario (ed.); Patera, Anthony (ed.); Rozza, Gianluigi (ed.); Urban, Karsten (ed.)
2017
Low-rank iterative methods for periodic projected Lyapunov equations and their application in model reduction of periodic descriptor systems. Zbl 1305.65158
2014
Dual pairs of generalized Lyapunov inequalities and balanced truncation of stochastic linear systems. Zbl 1364.93112
Benner, Peter; Damm, Tobias; Rodriguez Cruz, Yolanda Rocio
2017
Numerical linear algebra methods for linear differential-algebraic equations. Zbl 1343.65100
Benner, Peter; Losse, Philip; Mehrmann, Volker; Voigt, Matthias
2015
Solving stable Sylvester equations via rational iterative schemes. Zbl 1098.65041
Benner, Peter; Quintana-Ortí, Enrique S.; Quintana-Ortí, Gregorio
2006
On the parameter selection problem in the Newton-ADI iteration for large-scale Riccati equations. Zbl 1171.65402
Benner, Peter; Mena, Hermann; Saak, Jens
2008
Low-rank solution of unsteady diffusion equations with stochastic coefficients. Zbl 1325.65016
Benner, Peter; Onwunta, Akwum; Stoll, Martin
2015
Krylov-subspace based model reduction of nonlinear circuit models using bilinear and quadratic-linear approximations. Zbl 1246.78035
Benner, Peter; Breiten, Tobias
2012
Riccati-based boundary feedback stabilization of incompressible Navier-Stokes flows. Zbl 1312.93083
Bänsch, Eberhard; Benner, Peter; Saak, Jens; Weichelt, Heiko K.
2015
Frequency-limited balanced truncation with low-rank approximations. Zbl 1391.65123
Benner, Peter; Kürschner, Patrick; Saak, Jens
2016
Large-scale computation of $$\mathcal{L}_\infty$$-norms by a greedy subspace method. Zbl 1379.65020
Aliyev, Nicat; Benner, Peter; Mengi, Emre; Schwerdtner, Paul; Voigt, Matthias
2017
An inexact low-rank Newton-ADI method for large-scale algebraic Riccati equations. Zbl 1346.65017
Benner, Peter; Heinkenschloss, Matthias; Saak, Jens; Weichelt, Heiko K.
2016
Fast solution of Cahn-Hilliard variational inequalities using implicit time discretization and finite elements. Zbl 1349.65438
Bosch, Jessica; Stoll, Martin; Benner, Peter
2014
A Hamiltonian Krylov-Schur-type method based on the symplectic Lanczos process. Zbl 1219.65040
Benner, Peter; Faßbender, Heike; Stoll, Martin
2011
Optimal damping of selected eigenfrequencies using dimension reduction. Zbl 1289.70028
Benner, Peter; Tomljanović, Zoran; Truhar, Ninoslav
2013
An implicitly restarted symplectic Lanczos method for the symplectic eigenvalue problem. Zbl 0985.65026
Benner, Peter; Fassbender, Heike
2000
A mixed-precision algorithm for the solution of Lyapunov equations on hybrid CPU-GPU platforms. Zbl 1225.65037
Benner, Peter; Ezzatti, Pablo; Kressner, Daniel; Quintana-Ortí, Enrique S.; Remón, Alfredo
2011
Dimension reduction for damping optimization in linear vibrating systems. Zbl 1370.70041
Benner, Peter; Tomljanović, Zoran; Truhar, Ninoslav
2011
Parameter preserving model order reduction for MEMS applications. Zbl 1302.74063
Baur, U.; Benner, P.; Greiner, A.; Korvink, J. G.; Lienemann, J.; Moosmann, C.
2011
A structured pseudospectral method for $$\mathcal {H}_{\infty}$$-norm computation of large-scale descriptor systems. Zbl 1290.93083
Benner, Peter; Voigt, Matthias
2014
$$\mathcal L_\infty$$-norm computation for continuous-time descriptor systems using structured matrix pencils. Zbl 1369.93174
Benner, Peter; Sima, Vasile; Voigt, Matthias
2012
Stabilization of incompressible flow problems by Riccati-based feedback. Zbl 1356.93077
Bänsch, Eberhard; Benner, Peter
2012
Block-diagonal preconditioning for optimal control problems constrained by PDEs with uncertain inputs. Zbl 1382.65074
Benner, Peter; Onwunta, Akwum; Stoll, Martin
2016
A multishift algorithm for the numerical solution of algebraic Riccati equations. Zbl 0809.65040
Ammar, Gregory; Benner, Peter; Mehrmann, Volker
1993
A note on the numerical solution of complex Hamiltonian and skew-Hamiltonian eigenvalue problems. Zbl 0936.65045
Benner, Peter; Mehrmann, Volker; Xu, Hongguo
1999
Efficient solution of large-scale saddle point systems arising in Riccati-based boundary feedback stabilization of incompressible Stokes flow. Zbl 1290.76059
Benner, Peter; Saak, Jens; Stoll, Martin; Weichelt, Heiko K.
2013
Algorithm 854: Fortran 77 subroutines for computing the eigenvalues of Hamiltonian matrices. II. Zbl 1365.65091
Benner, Peter; Kressner, Daniel
2006
On optimality of approximate low rank solutions of large-scale matrix equations. Zbl 1292.65040
Benner, Peter; Breiten, Tobias
2014
LQG-balanced truncation low-order controller for stabilization of laminar flows. Zbl 1308.76105
Benner, Peter; Heiland, Jan
2015
Numerical algebra, matrix theory, differential-algebraic equations and control theory. Festschrift in honor of Volker Mehrmann. Zbl 1322.00048
Benner, Peter (ed.); Bollhöfer, Matthias (ed.); Kressner, Daniel (ed.); Mehl, Christian (ed.); Stykel, Tatjana (ed.)
2015
An efficient output error estimation for model order reduction of parametrized evolution equations. Zbl 1382.65281
Zhang, Yongjin; Feng, Lihong; Li, Suzhou; Benner, Peter
2015
Low-rank Newton-ADI methods for large nonsymmetric algebraic Riccati equations. Zbl 1336.93056
Benner, Peter; Kürschner, Patrick; Saak, Jens
2016
Model order reduction for coupled problems (survey). Zbl 1455.74003
Benner, Peter; Feng, Lihong
2015
Computational methods for linear-quadratic optimization. Zbl 0930.65075
Benner, Peter
1999
Numerical solution of discrete stable linear matrix equations on multicomputers. Zbl 1009.65039
Benner, Peter; Quintana-Ortí, Enrique S.; Quintana-Ortí, Gregorio
2002
Computing all or some eigenvalues of symmetric $$\mathcal{H}_{\ell}$$-matrices. Zbl 1387.65034
Benner, Peter; Mach, Thomas
2012
Partial realization of descriptor systems. Zbl 1113.93026
Benner, Peter; Sokolov, Viatcheslav I.
2006
Numerical linear algebra for model reduction in control and simulation. Zbl 1157.93337
Benner, Peter
2006
An $$\mathcal{H}_2$$-type error bound for balancing-related model order reduction of linear systems with Lévy noise. Zbl 1372.93185
Redmann, Martin; Benner, Peter
2017
Balancing based model reduction for structured index-2 unstable descriptor systems with application to flow control. Zbl 1330.93084
Benner, Peter; Saak, Jens; Monir Uddin, M.
2016
Fast iterative solution of the Bethe-Salpeter eigenvalue problem using low-rank and QTT tensor approximation. Zbl 1376.65045
Benner, Peter; Dolgov, Sergey; Khoromskaia, Venera; Khoromskij, Boris N.
2017
Some a posteriori error bounds for reduced-order modelling of (non-)parametrized linear systems. Zbl 1382.37105
Feng, Lihong; Antoulas, Athanasios C.; Benner, Peter
2017
A reduced basis method for microwave semiconductor devices with geometric variations. Zbl 1358.78055
Hess, Martin W.; Benner, Peter
2014
Evaluation of the linear matrix equation solvers in SLICOT. Zbl 1133.93317
Benner, Peter; Sima, Vasile; Slowik, Martin
2007
Solving algebraic Riccati equations on parallel computers using Newton’s method with exact line search. Zbl 0949.65041
Benner, P.; Byers, R.; Quintana-Ortí, E. S.; Quintana-Ortí, G.
2000
Numerical methods for linear quadratic and $$H_\infty$$ control problems. Zbl 0928.93017
Benner, Peter; Byers, Ralph; Mehrmann, Volker; Xu, Hongguo
1999
Parallel algorithms for LQ optimal control of discrete-time periodic linear systems. Zbl 1008.93035
Benner, Peter; Byers, Ralph; Mayo, Rafael; Quintana-Ortí, Enrique S.; Hernández, Vicente
2002
Parallel algorithms for model reduction of discrete-time systems. Zbl 1044.93012
Benner, P.; Quintana-Ortí, E. S.; Quintana-Ortí, G.
2003
Model reduction of an elastic crankshaft for elastic multibody simulations. Zbl 1275.70005
Nowakowski, Christine; Kürschner, Patrick; Eberhard, Peter; Benner, Peter
2013
Regularization of Poisson-Boltzmann-type equations with singular source terms using the range-separated tensor format. Zbl 1466.65180
Benner, Peter; Khoromskaia, Venera; Khoromskij, Boris; Kweyu, Cleophas; Stein, Matthias
2021
Model order reduction. Volume 1: System- and data-driven methods and algorithms (to appear). Zbl 07204874
Benner, Peter; Schilders, Wilhelmus; Grivet-Talocia, Stefano; Quarteroni, Alfio; Rozza, Gianluigi; Silveira, Luís Miguel
2021
Model order reduction. Volume 2: Snapshot-based methods and algorithms. Zbl 1455.93001
Benner, Peter; Grivet-Talocia, Stefano; Quarteroni, Alfio; Rozza, Gianluigi; Schilders, Wil; Silveira, Luís Miguel
2021
Model order reduction. Volume 3: Applications. Zbl 1455.93002
Benner, Peter; Grivet-Talocia, Stefano; Quarteroni, Alfio; Rozza, Gianluigi; Schilders, Wilhelmus; Silveira, Luís Miguel
2021
Implicit higher-order moment matching technique for model reduction of quadratic-bilinear systems. Zbl 1458.93040
Asif, Mian Mohammad Arsalan; Ahmad, Mian Ilyas; Benner, Peter; Feng, Lihong; Stykel, Tatjana
2021
Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms. Zbl 07337918
Benner, Peter; Goyal, Pawan; Kramer, Boris; Peherstorfer, Benjamin; Willcox, Karen
2020
Efficient solution of large-scale algebraic Riccati equations associated with index-2 DAEs via the inexact low-rank Newton-ADI method. Zbl 1462.76142
Benner, Peter; Heinkenschloss, Matthias; Saak, Jens; Weichelt, Heiko K.
2020
Identification of port-Hamiltonian systems from frequency response data. Zbl 1451.93063
Benner, Peter; Goyal, Pawan; Van Dooren, Paul
2020
A numerical comparison of different solvers for large-scale, continuous-time algebraic Riccati equations and LQR problems. Zbl 1437.65021
Benner, Peter; Bujanović, Zvonimir; Kürschner, Patrick; Saak, Jens
2020
Hankel-norm approximation of large-scale descriptor systems. Zbl 1441.93044
Benner, Peter; Werner, Steffen W. R.
2020
Index-aware MOR for gas transport networks. Zbl 1428.93025
Banagaaya, Nicodemus; Grundel, Sara; Benner, Peter
2020
Efficient numerical methods for gas network modeling and simulation. Zbl 1457.76013
Qiu, Yue; Grundel, Sara; Stoll, Martin; Benner, Peter
2020
A subspace framework for $$\mathcal{H}_\infty$$-norm minimization. Zbl 1461.93123
Aliyev, Nicat; Benner, Peter; Mengi, Emre; Voigt, Matthias
2020
Extended and improved criss-cross algorithms for computing the spectral value set abscissa and radius. Zbl 1457.93066
Benner, Peter; Mitchell, Tim
2019
Gas network benchmark models. Zbl 1445.76065
Benner, Peter; Grundel, Sara; Himpe, Christian; Huck, Christoph; Streubel, Tom; Tischendorf, Caren
2019
A bilinear $$\mathcal{H}_2$$ model order reduction approach to linear parameter-varying systems. Zbl 1434.93011
Benner, Peter; Cao, Xingang; Schilders, Wil
2019
Solution formulas for differential Sylvester and Lyapunov equations. Zbl 1432.15015
Behr, Maximilian; Benner, Peter; Heiland, Jan
2019
A low-rank inexact Newton-Krylov method for stochastic eigenvalue problems. Zbl 1420.65043
Benner, Peter; Onwunta, Akwum; Stoll, Martin
2019
Numerical solution of the infinite-dimensional LQR problem and the associated Riccati differential equations. Zbl 1444.65032
Benner, Peter; Mena, Hermann
2018
$$\mathcal H_2$$-quasi-optimal model order reduction for quadratic-bilinear control systems. Zbl 1418.93048
Benner, Peter; Goyal, Pawan; Gugercin, Serkan
2018
RADI: a low-rank ADI-type algorithm for large scale algebraic Riccati equations. Zbl 1385.65035
Benner, Peter; Bujanović, Zvonimir; Kürschner, Patrick; Saak, Jens
2018
Range-separated tensor format for many-particle modeling. Zbl 1446.65202
Benner, Peter; Khoromskaia, Venera; Khoromskij, Boris N.
2018
Singular perturbation approximation for linear systems with Lévy noise. Zbl 1394.60047
Redmann, Martin; Benner, Peter
2018
Faster and more accurate computation of the $$\mathcal{H}_\infty$$ norm via optimization. Zbl 1401.93087
Benner, Peter; Mitchell, Tim
2018
Space-time Galerkin POD with application in optimal control of semilinear partial differential equations. Zbl 1392.35323
Baumann, Manuel; Benner, Peter; Heiland, Jan
2018
Some remarks on the complex $$J$$-symmetric eigenproblem. Zbl 1392.65086
Benner, Peter; Faßbender, Heike; Yang, Chao
2018
Low-rank eigenvector compression of posterior covariance matrices for linear Gaussian inverse problems. Zbl 1398.65057
Benner, Peter; Qiu, Yue; Stoll, Martin
2018
$$\mathcal{L}_{\infty}$$-norm computation for large-scale descriptor systems using structured iterative eigensolvers. Zbl 1405.93028
Benner, Peter; Lowe, Ryan; Voigt, Matthias
2018
An index-aware parametric model order reduction method for parameterized quadratic differential-algebraic equations. Zbl 1426.65120
Banagaaya, Nicodemus; Benner, Peter; Feng, Lihong; Meuris, Peter; Schoenmaker, Wim
2018
An iterative model reduction scheme for quadratic-bilinear descriptor systems with an application to Navier-Stokes equations. Zbl 1416.76095
Benner, Peter; Goyal, Pawan
2018
Exponential stability and stabilization of extended linearizations via continuous updates of Riccati-based feedback. Zbl 1390.93655
Benner, P.; Heiland, J.
2018
Model reduction and approximation. Theory and algorithms. Zbl 1378.65010
Benner, Peter; Cohen, Albert; Ohlberger, Mario; Willcox, Karen
2017
Model order reduction for differential-algebraic equations: a survey. Zbl 1402.93069
Benner, Peter; Stykel, Tatjana
2017
Model reduction of parametrized systems. Selected contributions based on the presentations at the MoRePaS conference, SISSA, Trieste, Italy, October 13–16, 2015. Zbl 1381.65001
Benner, Peter; Ohlberger, Mario; Patera, Anthony; Rozza, Gianluigi; Urban, Karsten
2017
Dual pairs of generalized Lyapunov inequalities and balanced truncation of stochastic linear systems. Zbl 1364.93112
Benner, Peter; Damm, Tobias; Rodriguez Cruz, Yolanda Rocio
2017
Large-scale computation of $$\mathcal{L}_\infty$$-norms by a greedy subspace method. Zbl 1379.65020
Aliyev, Nicat; Benner, Peter; Mengi, Emre; Schwerdtner, Paul; Voigt, Matthias
2017
An $$\mathcal{H}_2$$-type error bound for balancing-related model order reduction of linear systems with Lévy noise. Zbl 1372.93185
Redmann, Martin; Benner, Peter
2017
Fast iterative solution of the Bethe-Salpeter eigenvalue problem using low-rank and QTT tensor approximation. Zbl 1376.65045
Benner, Peter; Dolgov, Sergey; Khoromskaia, Venera; Khoromskij, Boris N.
2017
Some a posteriori error bounds for reduced-order modelling of (non-)parametrized linear systems. Zbl 1382.37105
Feng, Lihong; Antoulas, Athanasios C.; Benner, Peter
2017
Adaptive symmetric interior penalty Galerkin method for boundary control problems. Zbl 1362.65122
Benner, Peter; Yücel, Hamdullah
2017
Krylov subspace-based model reduction for a class of bilinear descriptor systems. Zbl 1402.65083
Ahmad, Mian Ilyas; Benner, Peter; Goyal, Pawan
2017
Implicit Volterra series interpolation for model reduction of bilinear systems. Zbl 1377.93052
Ahmad, Mian Ilyas; Baur, Ulrike; Benner, Peter
2017
Structure preserving iterative methods for periodic projected Lyapunov equations and their application in model reduction of periodic descriptor systems. Zbl 1377.93053
2017
Reduced basis approximations for Maxwell’s equations in dispersive media. Zbl 1388.78018
Benner, Peter; Hess, Martin
2017
Truncated Gramians for bilinear systems and their advantages in model order reduction. Zbl 1384.93028
Benner, Peter; Goyal, Pawan; Redmann, Martin
2017
Trigonometric spline and spectral bounds for the solution of linear time-periodic systems. Zbl 1385.65045
Benner, Peter; Denißen, Jonas; Kohaupt, Ludwig
2017
On the solution of large-scale algebraic Riccati equations by using low-dimensional invariant subspaces. Zbl 1330.15017
Benner, Peter; Bujanović, Zvonimir
2016
Low-rank solvers for unsteady Stokes-Brinkman optimal control problem with random data. Zbl 1423.76329
Benner, Peter; Dolgov, Sergey; Onwunta, Akwum; Stoll, Martin
2016
Frequency-limited balanced truncation with low-rank approximations. Zbl 1391.65123
Benner, Peter; Kürschner, Patrick; Saak, Jens
2016
An inexact low-rank Newton-ADI method for large-scale algebraic Riccati equations. Zbl 1346.65017
Benner, Peter; Heinkenschloss, Matthias; Saak, Jens; Weichelt, Heiko K.
2016
Block-diagonal preconditioning for optimal control problems constrained by PDEs with uncertain inputs. Zbl 1382.65074
Benner, Peter; Onwunta, Akwum; Stoll, Martin
2016
Low-rank Newton-ADI methods for large nonsymmetric algebraic Riccati equations. Zbl 1336.93056
Benner, Peter; Kürschner, Patrick; Saak, Jens
2016
Balancing based model reduction for structured index-2 unstable descriptor systems with application to flow control. Zbl 1330.93084
Benner, Peter; Saak, Jens; Monir Uddin, M.
2016
Positive operators and stable truncation. Zbl 1335.15016
Benner, Peter; Damm, Tobias; Redmann, Martin; Rodriguez Cruz, Yolanda Rocio
2016
Multipoint interpolation of Volterra series and $$\mathcal{H}_2$$-model reduction for a family of bilinear descriptor systems. Zbl 1350.93024
Benner, Peter; Goyal, Pawan
2016
Parametric modeling and model order reduction for (electro-)thermal analysis of nanoelectronic structures. Zbl 1376.82104
Feng, Lihong; Yue, Yao; Banagaaya, Nicodemus; Meuris, Peter; Schoenmaker, Wim; Benner, Peter
2016
Structure preserving model order reduction of large sparse second-order index-1 systems and application to a mechatronics model. Zbl 1348.93025
Benner, Peter; Saak, Jens; Uddin, M. Monir
2016
Reduced basis modeling for uncertainty quantification of electromagnetic problems in stochastically varying domains. Zbl 1383.78050
Benner, Peter; Hess, Martin W.
2016
A survey of projection-based model reduction methods for parametric dynamical systems. Zbl 1339.37089
Benner, Peter; Gugercin, Serkan; Willcox, Karen
2015
Model reduction for stochastic systems. Zbl 1331.65017
Benner, Peter; Redmann, Martin
2015
Two-sided projection methods for nonlinear model order reduction. Zbl 1312.93016
Benner, Peter; Breiten, Tobias
2015
Recycling BiCGSTAB with an application to parametric model order reduction. Zbl 1325.65044
Ahuja, Kapil; Benner, Peter; de Sturler, Eric; Feng, Lihong
2015
Numerical linear algebra methods for linear differential-algebraic equations. Zbl 1343.65100
Benner, Peter; Losse, Philip; Mehrmann, Volker; Voigt, Matthias
2015
Low-rank solution of unsteady diffusion equations with stochastic coefficients. Zbl 1325.65016
Benner, Peter; Onwunta, Akwum; Stoll, Martin
2015
Riccati-based boundary feedback stabilization of incompressible Navier-Stokes flows. Zbl 1312.93083
Bänsch, Eberhard; Benner, Peter; Saak, Jens; Weichelt, Heiko K.
2015
LQG-balanced truncation low-order controller for stabilization of laminar flows. Zbl 1308.76105
Benner, Peter; Heiland, Jan
2015
Numerical algebra, matrix theory, differential-algebraic equations and control theory. Festschrift in honor of Volker Mehrmann. Zbl 1322.00048
Benner, Peter; Bollhöfer, Matthias; Kressner, Daniel; Mehl, Christian; Stykel, Tatjana
2015
An efficient output error estimation for model order reduction of parametrized evolution equations. Zbl 1382.65281
Zhang, Yongjin; Feng, Lihong; Li, Suzhou; Benner, Peter
2015
Model order reduction for coupled problems (survey). Zbl 1455.74003
Benner, Peter; Feng, Lihong
2015
Adaptive discontinuous Galerkin methods for state constrained optimal control problems governed by convection diffusion equations. Zbl 1333.49047
Yücel, Hamdullah; Benner, Peter
2015
Parametric model order reduction of thermal models using the bilinear interpolatory rational Krylov algorithm. Zbl 1310.93038
Bruns, Angelika; Benner, Peter
2015
Accelerating PDE constrained optimization by the reduced basis method: application to batch chromatography. Zbl 1352.49026
Zhang, Yongjin; Feng, Lihong; Li, Suzhou; Benner, Peter
2015
Approximation and model order reduction for second order systems with Levy-noise. Zbl 1336.34082
Benner, Peter; Redmann, Martin
2015
Reduced-order modeling and ROM-based optimization of batch chromatography. Zbl 1328.65220
Benner, Peter; Feng, Lihong; Li, Suzhou; Zhang, Yongjin
2015
Theory and numerical solution of differential and algebraic Riccati equations. Zbl 1322.65077
Benner, Peter
2015
Model order reduction for a family of linear systems with applications in parametric and uncertain systems. Zbl 1310.93037
Benner, Peter; Grundel, Sara
2015
Distributed optimal control problems governed by coupled convection dominated PDEs with control constraints. Zbl 1328.65145
Yücel, Hamdullah; Benner, Peter
2015
Parametric model order reduction with a small $$\mathcal H_2$$-error using radial basis functions. Zbl 1348.65096
Benner, Peter; Grundel, Sara; Hornung, Nils
2015
Matrix equations and model reduction. Zbl 1332.65083
Benner, Peter; Breiten, Tobias; Feng, Lihong
2015
A discontinuous Galerkin method for optimal control problems governed by a system of convection-diffusion PDEs with nonlinear reaction terms. Zbl 1443.65380
Yücel, Hamdullah; Stoll, Martin; Benner, Peter
2015
Model order reduction for linear and nonlinear systems: a system-theoretic perspective. Zbl 1348.93075
Baur, Ulrike; Benner, Peter; Feng, Lihong
2014
Self-generating and efficient shift parameters in ADI methods for large Lyapunov and Sylvester equations. Zbl 1312.65068
Benner, Peter; Kürschner, Patrick; Saak, Jens
2014
Model order reduction for PDE constrained optimization. Zbl 1327.49043
Benner, Peter; Sachs, Ekkehard; Volkwein, Stefan
2014
A robust algorithm for parametric model order reduction based on implicit moment matching. Zbl 1312.65109
Benner, Peter; Feng, Lihong
2014
Model order reduction of differential algebraic equations arising from the simulation of gas transport networks. Zbl 1319.65077
Grundel, Sara; Jansen, Lennart; Hornung, Nils; Clees, Tanja; Tischendorf, Caren; Benner, Peter
2014
Computing real low-rank solutions of Sylvester equations by the factored ADI method. Zbl 1364.65093
Benner, Peter; Kürschner, Patrick
2014
Low-rank iterative methods for periodic projected Lyapunov equations and their application in model reduction of periodic descriptor systems. Zbl 1305.65158
2014
Fast solution of Cahn-Hilliard variational inequalities using implicit time discretization and finite elements. Zbl 1349.65438
Bosch, Jessica; Stoll, Martin; Benner, Peter
2014
A structured pseudospectral method for $$\mathcal {H}_{\infty}$$-norm computation of large-scale descriptor systems. Zbl 1290.93083
Benner, Peter; Voigt, Matthias
2014
On optimality of approximate low rank solutions of large-scale matrix equations. Zbl 1292.65040
Benner, Peter; Breiten, Tobias
2014
A reduced basis method for microwave semiconductor devices with geometric variations. Zbl 1358.78055
Hess, Martin W.; Benner, Peter
2014
Numerical solution of projected algebraic Riccati equations. Zbl 1298.65076
Benner, Peter; Stykel, Tatjana
2014
Trends in PDE constrained optimization. Zbl 1306.49001
Leugering, Günter; Benner, Peter; Engell, Sebastian; Griewank, Andreas; Harbrecht, Helmut; Hinze, Michael; Rannacher, Rolf; Ulbrich, Stefan
2014
A non-conforming composite quadrilateral finite element pair for feedback stabilization of the Stokes equations. Zbl 1303.65095
Benner, P.; Saak, J.; Schieweck, F.; Skrzypacz, P.; Weichelt, H. K.
2014
Optimal control-based feedback stabilization of multi-field flow problems. Zbl 1327.49061
Bänsch, Eberhard; Benner, Peter; Saak, Jens; Weichelt, Heiko K.
2014
On the squared Smith method for large-scale Stein equations. Zbl 1340.65073
Benner, Peter; El Khoury, Grece; Sadkane, Miloud
2014
Rational interpolation methods for symmetric Sylvester equations. Zbl 1312.65067
Benner, Peter; Breiten, Tobias
2014
Large-scale networks in engineering and life sciences. Based on the summer school, Magdeburg, Germany, September 26–30, 2011. Zbl 1300.90004
Benner, Peter; Findeisen, Rolf; Flockerzi, Dietrich; Reichl, Udo; Sundmacher, Kai
2014
Efficient solvers for large-scale saddle point systems arising in feedback stabilization of multi-field flow problems. Zbl 1329.76105
Benner, Peter; Saak, Jens; Stoll, Martin; Weichelt, Heiko K.
2014
Numerical solution of large and sparse continuous time algebraic matrix Riccati and Lyapunov equations: a state of the art survey. Zbl 1279.65044
Benner, Peter; Saak, Jens
2013
...and 95 more Documents
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#### Cited by 1,335 Authors

 128 Benner, Peter 30 Mehrmann, Volker 26 Gugercin, Serkan 26 Jiang, Yaolin 19 Kressner, Daniel 18 Peherstorfer, Benjamin 17 Kürschner, Patrick 17 Saak, Jens 16 Redmann, Martin 16 Simoncini, Valeria 16 Stoll, Martin 15 Faßbender, Heike 15 Stykel, Tatjana 13 Beattie, Christopher A. 13 Breiten, Tobias 13 Quintana-Ortí, Enrique S. 13 Willcox, Karen E. 12 Feng, Lihong 12 Mena, Hermann 11 Eberhard, Peter 11 Khoromskij, Boris N. 11 Pulch, Roland 11 Rozza, Gianluigi 10 Dolgov, Sergey V. 10 King-wah Chu, Eric 10 Kutz, J. Nathan 10 Tomljanović, Zoran 9 Goyal, Pawan 9 Haasdonk, Bernard 9 Jbilou, Khalide 9 Lin, Wen-Wei 9 Truhar, Ninoslav 9 Xu, Hongguo 8 Brunton, Steven L. 8 Fan, Hung-Yuan 8 Van Dooren, Paul M. 8 Watkins, David S. 8 Xu, Kangli 7 Alla, Alessandro 7 Antoulas, Athanasios C. 7 Grundel, Sara 7 Hajarian, Masoud 7 Heinkenschloss, Matthias 7 Ma, Changfeng 7 Mehl, Christian 7 Poloni, Federico G. 7 Singler, John R. 7 Voigt, Matthias 7 Wang, Xiaolong 6 Baur, Ulrike 6 de Sturler, Eric 6 Fehr, Jörg 6 Iskakov, Alekseĭ Borisovich 6 Khoromskaia, Venera 6 Krämer, Boris 6 Kunisch, Karl 6 Li, Rencang 6 Lohmann, Boris 6 Manzoni, Andrea 6 Palitta, Davide 6 Quarteroni, Alfio M. 6 Robol, Leonardo 6 Xiao, Zhihua 5 Chen, Xiaoshan 5 Drmač, Zlatko 5 Freitag, Melina A. 5 Gosea, Ion Victor 5 Hesthaven, Jan S. 5 Huang, Ting-Zhu 5 Jarlebring, Elias 5 Mitchell, Tim 5 Nouy, Anthony 5 Quintana-Ortí, Gregorio 5 Reis, Timo 5 Uddin, Mohammad Monir 5 Unger, Benjamin 5 Volkwein, Stefan 5 Wei, Yimin 5 Weng, Peter Chang-Yi 5 Yadykin, I. B. 5 Yücel, Hamdullah 4 Ahmad, Mian Ilyas 4 Ballarin, Francesco 4 Banagaaya, Nicodemus 4 Buchot, Jean-Marie 4 Bujanović, Zvonimir 4 Byers, Ralph 4 Damm, Tobias 4 Desmet, Wim 4 Elman, Howard C. 4 Fröhlich, Benjamin 4 Guo, Chun-Hua 4 Hartmann, Carsten 4 Heiland, Jan 4 Heyouni, Mohammed 4 Himpe, Christian 4 Holzwarth, Philip 4 Hossain, Mohammad-Sahadet 4 Lee, Kookjin 4 Lv, Lingling ...and 1,235 more Authors
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#### Cited in 171 Serials

 81 Linear Algebra and its Applications 71 SIAM Journal on Scientific Computing 50 Journal of Computational and Applied Mathematics 38 SIAM Journal on Matrix Analysis and Applications 36 Advances in Computational Mathematics 32 Computer Methods in Applied Mechanics and Engineering 31 Journal of Computational Physics 26 Journal of the Franklin Institute 24 Applied Mathematics and Computation 22 Systems & Control Letters 21 Numerical Algorithms 21 Numerical Linear Algebra with Applications 20 Applied Numerical Mathematics 20 Journal of Scientific Computing 19 SIAM/ASA Journal on Uncertainty Quantification 18 International Journal of Control 18 BIT 17 Computers & Mathematics with Applications 16 Numerische Mathematik 16 Mathematical and Computer Modelling of Dynamical Systems 14 SIAM Journal on Control and Optimization 13 Automatica 9 Mathematics of Computation 9 Computational and Applied Mathematics 8 Mathematical Problems in Engineering 8 Vietnam Journal of Mathematics 7 Applied Mathematics Letters 7 Applied Mathematical Modelling 7 Numerical Algebra, Control and Optimization 6 Computational Mechanics 6 Automation and Remote Control 6 International Journal of Computer Mathematics 6 ETNA. Electronic Transactions on Numerical Analysis 6 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 5 Linear and Multilinear Algebra 5 International Journal for Numerical Methods in Engineering 5 Mathematics and Computers in Simulation 5 SIAM Journal on Numerical Analysis 5 MCSS. Mathematics of Control, Signals, and Systems 5 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 5 Multibody System Dynamics 5 Computational Methods in Applied Mathematics 4 Computers and Fluids 4 SIAM Review 4 Doklady Mathematics 4 SIAM Journal on Applied Dynamical Systems 4 Multiscale Modeling & Simulation 4 GAMM-Mitteilungen 4 Algorithms 3 Journal of Fluid Mechanics 3 Journal of Mathematical Analysis and Applications 3 SIAM Journal on Optimization 3 Computational Optimization and Applications 3 European Journal of Control 3 Computing and Visualization in Science 3 Journal of Industrial and Management Optimization 3 Asian Journal of Control 3 Journal of Mathematics in Industry 3 East Asian Journal on Applied Mathematics 2 International Journal of Systems Science 2 ACM Transactions on Mathematical Software 2 Applied Mathematics and Optimization 2 Calcolo 2 Journal of Optimization Theory and Applications 2 Circuits, Systems, and Signal Processing 2 Applied Mathematics and Mechanics. (English Edition) 2 COMPEL 2 Japan Journal of Industrial and Applied Mathematics 2 Journal of Mathematical Sciences (New York) 2 Turkish Journal of Mathematics 2 Nonlinear Dynamics 2 Optimization Methods & Software 2 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 2 Chaos 2 Discrete Dynamics in Nature and Society 2 Communications in Nonlinear Science and Numerical Simulation 2 Computational Geosciences 2 Archives of Computational Methods in Engineering 2 Discrete and Continuous Dynamical Systems. Series B 2 Journal of Applied Mathematics 2 Acta Numerica 2 Advances in Difference Equations 2 Complex Analysis and Operator Theory 2 Frontiers of Mathematics in China 2 Mathematical Control and Related Fields 2 Journal of Applied Analysis and Computation 2 Evolution Equations and Control Theory 2 Journal of Computational Dynamics 2 Electronic Research Archive 1 Acta Mechanica 1 Biological Cybernetics 1 Inverse Problems 1 Journal of Engineering Mathematics 1 Theoretical and Computational Fluid Dynamics 1 Annales de l’Institut Fourier 1 Computing 1 Journal of Approximation Theory 1 Proceedings of the American Mathematical Society 1 Topology and its Applications 1 Optimal Control Applications & Methods ...and 71 more Serials
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#### Cited in 50 Fields

 650 Numerical analysis (65-XX) 335 Systems theory; control (93-XX) 273 Linear and multilinear algebra; matrix theory (15-XX) 135 Partial differential equations (35-XX) 103 Calculus of variations and optimal control; optimization (49-XX) 79 Fluid mechanics (76-XX) 50 Ordinary differential equations (34-XX) 48 Dynamical systems and ergodic theory (37-XX) 46 Mechanics of deformable solids (74-XX) 41 Probability theory and stochastic processes (60-XX) 37 Operations research, mathematical programming (90-XX) 31 Operator theory (47-XX) 31 Optics, electromagnetic theory (78-XX) 30 Statistics (62-XX) 30 Mechanics of particles and systems (70-XX) 25 Approximations and expansions (41-XX) 25 Computer science (68-XX) 14 Classical thermodynamics, heat transfer (80-XX) 13 Biology and other natural sciences (92-XX) 12 Statistical mechanics, structure of matter (82-XX) 12 Information and communication theory, circuits (94-XX) 7 Functions of a complex variable (30-XX) 7 Functional analysis (46-XX) 7 Geophysics (86-XX) 6 Combinatorics (05-XX) 5 General and overarching topics; collections (00-XX) 4 History and biography (01-XX) 4 Group theory and generalizations (20-XX) 4 Special functions (33-XX) 4 Difference and functional equations (39-XX) 4 Quantum theory (81-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Algebraic geometry (14-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Differential geometry (53-XX) 2 Number theory (11-XX) 2 Real functions (26-XX) 2 General topology (54-XX) 2 Algebraic topology (55-XX) 1 Commutative algebra (13-XX) 1 Associative rings and algebras (16-XX) 1 Nonassociative rings and algebras (17-XX) 1 Topological groups, Lie groups (22-XX) 1 Measure and integration (28-XX) 1 Sequences, series, summability (40-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral equations (45-XX) 1 Convex and discrete geometry (52-XX) 1 Global analysis, analysis on manifolds (58-XX)

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