## 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 · IdRef
 Documents Indexed: 261 Publications since 1993, including 1 Book 21 Contributions as Editor Co-Authors: 214 Co-Authors with 272 Joint Publications 3,837 Co-Co-Authors
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### Co-Authors

 10 single-authored 25 Feng, Lihong 24 Saak, Jens 21 Quintana-Ortí, Enrique S. 18 Faßbender, Heike 14 Grundel, Sara M. 14 Mehrmann, Volker 14 Stoll, Martin 12 Byers, Ralph 12 Quintana-Ortí, Gregorio 11 Goyal, Pawan 10 Breiten, Tobias 10 Kürschner, Patrick 9 Baur, Ulrike 8 Heiland, Jan 8 Kressner, Daniel 8 Xu, Hongguo 7 Rozza, Gianluigi 7 Stykel, Tatjana 7 Voigt, Matthias 7 Weichelt, Heiko K. 7 Werner, Steffen W. R. 6 Banagaaya, Nicodemus 6 Gugercin, Serkan 6 Mayo, Rafael 6 Mena, Hermann 6 Redmann, Martin 6 Schilders, Wil H. A. 6 Trautwein, Christoph 5 Grivet-Talocia, Stefano 5 Himpe, Christian 5 Mach, Thomas 5 Pontes Duff, Igor 5 Quarteroni, Alfio M. 5 Silveira, Luís Miguel 5 Yücel, Hamdullah 4 Ahmad, Mian Ilyas 4 Damm, Tobias 4 Hess, Martin Wilfried 4 Hinze, Michael 4 Khoromskaia, Venera 4 Khoromskiĭ, Boris Nikolaevich 4 Onwunta, Akwum 4 Remón, Alfredo 4 Truhar, Ninoslav 4 Zuyev, Aleksandr Leonidovich 3 Antoulas, Athanasios C. 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 Schneider, René 3 Schoenmaker, Wim 3 Seidel-Morgenstern, Andreas 3 Sima, Vasile 3 Tischendorf, Caren 3 Watkins, David S. 3 Willcox, Karen E. 3 Zhang, Yongjin 2 Aliyev, Nicat 2 Beattie, Christopher A. 2 Behr, Maximilian 2 Cao, Xingang 2 Castillo, Maribel 2 Chellappa, Sridhar 2 Clees, Tanja 2 Embree, Mark 2 Heinkenschloss, Matthias 2 Hornung, Nils 2 Korvink, Jan G. 2 Losse, Philip 2 Mengi, Emre 2 Mlinarić, Petar 2 Patera, Anthony T. 2 Penke, Carolin 2 Qiu, Yue 2 Rodriguez Cruz, Yolanda Rocio 2 Sadkane, Miloud 2 Schneider, André 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 Alì, Giuseppe 1 Ammar, Gregory S. 1 Asif, Mian Mohammad Arsalan 1 Baldin, Anton 1 Ballard, Grey M. 1 Baran, Björn 1 Barrachina, Sergio ...and 114 more Co-Authors
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### Serials

 17 SIAM Journal on Scientific Computing 15 Linear Algebra and its Applications 13 ETNA. Electronic Transactions on Numerical Analysis 10 SIAM Journal on Matrix Analysis and Applications 10 Advances in Computational Mathematics 7 Mathematical and Computer Modelling of Dynamical Systems 7 PAMM. Proceedings in Applied Mathematics and Mechanics 6 IEEE Transactions on Automatic Control 6 Journal of Computational and Applied Mathematics 6 Numerical Algorithms 6 Numerical Linear Algebra with Applications 5 Systems & Control Letters 4 Numerische Mathematik 4 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 3 Computer Methods in Applied Mechanics and Engineering 3 Journal of Computational Physics 3 MCSS. Mathematics of Control, Signals, and Systems 3 Computational Optimization and Applications 3 GAMM-Mitteilungen 2 Computers & Mathematics with Applications 2 International Journal of Control 2 Journal of the Franklin Institute 2 Mitteilungen der Deutschen Mathematiker-Vereinigung (DMV) 2 ACM Transactions on Mathematical Software 2 Applied Mathematics and Computation 2 Automatica 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 Journal of Scientific Computing 2 Applied Mathematical Modelling 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 Journal of Mathematics in Industry 2 SIAM/ASA Journal on Uncertainty Quantification 1 IMA Journal of Numerical Analysis 1 International Journal of Systems Science 1 Journal of Mathematical Analysis and Applications 1 Applied Mathematics and Optimization 1 Calcolo 1 Mathematische Nachrichten 1 SIAM Journal on Control and Optimization 1 COMPEL 1 Applied Mathematics Letters 1 Journal of Parallel and Distributed Computing 1 The Journal of Supercomputing 1 International Journal of Computer Mathematics 1 SIAM Review 1 Journal of Dynamics and Differential Equations 1 International Journal of Robust and Nonlinear Control 1 Analele Științifice ale Universității “Ovidius” Constanța. 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 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

 176 Numerical analysis (65-XX) 133 Systems theory; control (93-XX) 69 Linear and multilinear algebra; matrix theory (15-XX) 33 Calculus of variations and optimal control; optimization (49-XX) 30 Partial differential equations (35-XX) 24 Fluid mechanics (76-XX) 21 General and overarching topics; collections (00-XX) 16 Ordinary differential equations (34-XX) 15 Optics, electromagnetic theory (78-XX) 12 Dynamical systems and ergodic theory (37-XX) 10 Probability theory and stochastic processes (60-XX) 10 Computer science (68-XX) 8 Mechanics of deformable solids (74-XX) 5 Classical thermodynamics, heat transfer (80-XX) 5 Statistical mechanics, structure of matter (82-XX) 5 Biology and other natural sciences (92-XX) 4 Mechanics of particles and systems (70-XX) 4 Operations research, mathematical programming (90-XX) 3 Approximations and expansions (41-XX) 3 Information and communication theory, circuits (94-XX) 2 History and biography (01-XX) 2 Combinatorics (05-XX) 2 Geophysics (86-XX) 1 Special functions (33-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

221 Publications have been cited 2,618 times in 1,242 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
Lyapunov equations, energy functionals, and model order reduction of bilinear and stochastic systems. Zbl 1217.93158
Benner, Peter; Damm, Tobias
2011
Model order reduction for linear and nonlinear systems: a system-theoretic perspective. Zbl 1348.93075
Baur, Ulrike; Benner, Peter; Feng, Lihong
2014
Dimension reduction of large-scale systems. Proceedings of a workshop, Oberwolfach, Germany, October 19–25, 2003. Zbl 1066.65004
2005
On the ADI method for Sylvester equations. Zbl 1176.65050
Benner, Peter; Li, Ren-Cang; Truhar, Ninoslav
2009
Interpolatory projection methods for parameterized model reduction. Zbl 1254.93032
Baur, Ulrike; Beattie, Christopher; Benner, Peter; Gugercin, Serkan
2011
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
Interpolation-based $${\mathcal H}_2$$-model reduction of bilinear control systems. Zbl 1256.93027
Benner, Peter; Breiten, Tobias
2012
Model reduction and approximation. Theory and algorithms. Zbl 1378.65010
2017
Solving stable generalized Lyapunov equations with the matrix sign function. Zbl 0940.65035
Benner, Peter; Quintana-Ortí, Enrique S.
1999
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
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
SLICOT – a subroutine library in systems and control theory. Zbl 1051.93500
Benner, Peter; Mehrmann, Volker; Sima, Vasile; Van Huffel, Sabine; Varga, Andras
1999
Two-sided projection methods for nonlinear model order reduction. Zbl 1312.93016
Benner, Peter; Breiten, Tobias
2015
Numerical computation of deflating subspaces of skew-Hamiltonian/Hamiltonian pencils. Zbl 1035.49022
Benner, Peter; Byers, Ralph; Mehrmann, Volker; Xu, Hongguo
2002
Cross-Gramian based model reduction for data-sparse systems. Zbl 1170.93315
Baur, Ulrike; Benner, Peter
2008
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
Efficient handling of complex shift parameters in the low-rank Cholesky factor ADI method. Zbl 1267.65047
Benner, Peter; Kürschner, Patrick; Saak, Jens
2013
Factorized solution of Lyapunov equations based on hierarchical matrix arithmetic. Zbl 1111.65039
Baur, U.; Benner, P.
2006
An exact line search method for solving generalized continuous-time algebraic Riccati equations. Zbl 0908.93026
Benner, Peter; Byers, Ralph
1998
$$\mathcal H_2$$-quasi-optimal model order reduction for quadratic-bilinear control systems. Zbl 1418.93048
Benner, Peter; Goyal, Pawan; Gugercin, Serkan
2018
Rosenbrock methods for solving Riccati differential equations. Zbl 1369.65088
Benner, Peter; Mena, Hermann
2013
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
A robust algorithm for parametric model order reduction based on implicit moment matching. Zbl 1312.65109
Benner, Peter; Feng, Lihong
2014
Model order reduction for PDE constrained optimization. Zbl 1327.49043
Benner, Peter; Sachs, Ekkehard; Volkwein, Stefan
2014
Model reduction for stochastic systems. Zbl 1331.65017
Benner, Peter; Redmann, Martin
2015
A semi-discretized heat transfer model for optimal cooling of steel profiles. Zbl 1170.80341
Benner, Peter; Saak, Jens
2005
An improved numerical method for balanced truncation for symmetric second-order systems. Zbl 1305.93043
Benner, Peter; Kürschner, Patrick; Saak, Jens
2013
Model order reduction for differential-algebraic equations: a survey. Zbl 1402.93069
Benner, Peter; Stykel, Tatjana
2017
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
Skew-Hamiltonian and Hamiltonian eigenvalue problems: theory, algorithms and applications. Zbl 1069.65034
Benner, Peter; Kressner, Daniel; Mehrmann, Volker
2005
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
Numerical solution of the infinite-dimensional LQR problem and the associated Riccati differential equations. Zbl 1444.65032
Benner, Peter; Mena, Hermann
2018
Cholesky-like factorizations of skew-symmetric matrices. Zbl 0963.65033
Benner, Peter; Byers, Ralph; Fassbender, Heike; Mehrmann, Volker; Watkins, David
2000
On the numerical solution of large-scale sparse discrete-time Riccati equations. Zbl 1230.65070
Benner, Peter; Faßbender, Heike
2011
Efficient balancing-based MOR for large-scale second-order systems. Zbl 1221.93039
Benner, Peter; Saak, Jens
2011
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
Low-rank solution of unsteady diffusion equations with stochastic coefficients. Zbl 1325.65016
Benner, Peter; Onwunta, Akwum; Stoll, 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
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
2017
Contributions to the numerical solution of algebraic Riccati equations and related eigenvalue problems. Zbl 0896.65047
Benner, Peter
1997
Generalised tangential interpolation for model reduction of discrete-time MIMO bilinear systems. Zbl 1230.93010
Benner, P.; Breiten, T.; Damm, T.
2011
A robust numerical method for the $$\gamma$$-iteration in $$H_{\infty}$$ control. Zbl 1124.93022
Benner, Peter; Byers, Ralph; Mehrmann, Volker; Xu, Hongguo
2007
Computing real low-rank solutions of Sylvester equations by the factored ADI method. Zbl 1364.65093
Benner, Peter; Kürschner, Patrick
2014
Recycling BiCGSTAB with an application to parametric model order reduction. Zbl 1325.65044
Ahuja, Kapil; Benner, Peter; de Sturler, Eric; Feng, Lihong
2015
Riccati-based boundary feedback stabilization of incompressible Navier-Stokes flows. Zbl 1312.93083
Bänsch, Eberhard; Benner, Peter; Saak, Jens; Weichelt, Heiko K.
2015
Evaluating products of matrix pencils and collapsing matrix products. Zbl 1055.65053
Benner, Peter; Byers, Ralph
2001
On the solution of large-scale algebraic Riccati equations by using low-dimensional invariant subspaces. Zbl 1330.15017
Benner, Peter; Bujanović, Zvonimir
2016
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
Low-rank iterative methods for periodic projected Lyapunov equations and their application in model reduction of periodic descriptor systems. Zbl 1305.65158
2014
Perturbation analysis for the eigenvalue problem of a formal product of matrices. Zbl 1003.65032
Benner, Peter; Mehrmann, Volker; Xu, Hongguo
2002
Frequency-limited balanced truncation with low-rank approximations. Zbl 1391.65123
Benner, Peter; Kürschner, Patrick; Saak, Jens
2016
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
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
Fast solution of Cahn-Hilliard variational inequalities using implicit time discretization and finite elements. Zbl 1349.65438
Bosch, Jessica; Stoll, Martin; Benner, Peter
2014
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
Numerical linear algebra methods for linear differential-algebraic equations. Zbl 1343.65100
Benner, Peter; Losse, Philip; Mehrmann, Volker; Voigt, Matthias
2015
Block-diagonal preconditioning for optimal control problems constrained by PDEs with uncertain inputs. Zbl 1382.65074
Benner, Peter; Onwunta, Akwum; Stoll, Martin
2016
A Hamiltonian Krylov-Schur-type method based on the symplectic Lanczos process. Zbl 1219.65040
Benner, Peter; Faßbender, Heike; Stoll, Martin
2011
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
Krylov-subspace based model reduction of nonlinear circuit models using bilinear and quadratic-linear approximations. Zbl 1246.78035
Benner, Peter; Breiten, Tobias
2012
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
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
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
Solving stable Sylvester equations via rational iterative schemes. Zbl 1098.65041
Benner, Peter; Quintana-Ortí, Enrique S.; Quintana-Ortí, Gregorio
2006
LQG-balanced truncation low-order controller for stabilization of laminar flows. Zbl 1308.76105
Benner, Peter; Heiland, Jan
2015
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
$$\mathcal L_\infty$$-norm computation for continuous-time descriptor systems using structured matrix pencils. Zbl 1369.93174
Benner, Peter; Sima, Vasile; Voigt, Matthias
2012
Optimal damping of selected eigenfrequencies using dimension reduction. Zbl 1289.70028
Benner, Peter; Tomljanović, Zoran; Truhar, Ninoslav
2013
Model order reduction for coupled problems (survey). Zbl 1455.74003
Benner, Peter; Feng, Lihong
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
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
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
A note on the numerical solution of complex Hamiltonian and skew-Hamiltonian eigenvalue problems. Zbl 0936.65045
Benner, Peter; Mehrmann, Volker; Xu, Hongguo
1999
Subspace recycling accelerates the parametric macro-modeling of MEMS. Zbl 1352.74479
Feng, Lihong; Benner, Peter; Korvink, Jan G.
2013
Stabilization of incompressible flow problems by Riccati-based feedback. Zbl 1356.93077
Bänsch, Eberhard; Benner, Peter
2012
Dimension reduction for damping optimization in linear vibrating systems. Zbl 1370.70041
Benner, Peter; Tomljanović, Zoran; Truhar, Ninoslav
2011
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
A multishift algorithm for the numerical solution of algebraic Riccati equations. Zbl 0809.65040
Ammar, Gregory; Benner, Peter; Mehrmann, Volker
1993
Partial realization of descriptor systems. Zbl 1113.93026
Benner, Peter; Sokolov, Viatcheslav I.
2006
Computational methods for linear-quadratic optimization. Zbl 0930.65075
Benner, Peter
1999
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
A reduced basis method for microwave semiconductor devices with geometric variations. Zbl 1358.78055
Hess, Martin W.; Benner, Peter
2014
A note on projection techniques for model order reduction of bilinear systems. Zbl 1152.65332
Feng, Lihong; Benner, Peter
2007
Low-rank Newton-ADI methods for large nonsymmetric algebraic Riccati equations. Zbl 1336.93056
Benner, Peter; Kürschner, Patrick; Saak, Jens
2016
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
On optimality of approximate low rank solutions of large-scale matrix equations. Zbl 1292.65040
Benner, Peter; Breiten, Tobias
2014
Krylov subspace-based model reduction for a class of bilinear descriptor systems. Zbl 1402.65083
Ahmad, Mian Ilyas; Benner, Peter; Goyal, Pawan
2017
Computing all or some eigenvalues of symmetric $$\mathcal{H}_{\ell}$$-matrices. Zbl 1387.65034
Benner, Peter; Mach, Thomas
2012
Numerical algebra, matrix theory, differential-algebraic equations and control theory. Festschrift in honor of Volker Mehrmann. Zbl 1322.00048
2015
Numerical solution of discrete stable linear matrix equations on multicomputers. Zbl 1009.65039
Benner, Peter; Quintana-Ortí, Enrique S.; Quintana-Ortí, Gregorio
2002
Numerical linear algebra for model reduction in control and simulation. Zbl 1157.93337
Benner, Peter
2006
Positive operators and stable truncation. Zbl 1335.15016
Benner, Peter; Damm, Tobias; Redmann, Martin; Rodriguez Cruz, Yolanda Rocio
2016
Range-separated tensor format for many-particle modeling. Zbl 1446.65202
Benner, Peter; Khoromskaia, Venera; Khoromskij, Boris N.
2018
Parallel algorithms for tensor train arithmetic. Zbl 1484.65088
Al Daas, Hussam; Ballard, Grey; Benner, Peter
2022
Gramians, energy functionals, and balanced truncation for linear dynamical systems with quadratic outputs. Zbl 07480828
Benner, Peter; Goyal, Pawan; Pontes Duff, Igor
2022
Efficient and accurate algorithms for solving the Bethe-Salpeter eigenvalue problem for crystalline systems. Zbl 1473.65044
Benner, Peter; Penke, Carolin
2022
Interpolation-based model order reduction for polynomial systems. Zbl 1458.93041
Benner, Peter; Goyal, Pawan
2021
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: basic concepts and notation. Zbl 1480.93046
Benner, Peter; Grivet-Talocia, Stefano; Quarteroni, Alfio; Rozza, Gianluigi; Schilders, Wil; 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
Model order reduction. Volume 1: System- and data-driven methods and algorithms. Zbl 1473.93004
2021
Model order reduction. Volume 2: Snapshot-based methods and algorithms. Zbl 1455.93001
2021
Model order reduction. Volume 3: Applications. Zbl 1455.93002
2021
Matrix equations, sparse solvers: M-M.E.S.S.-2.0.1 – philosophy, features, and application for (parametric) model order reduction. Zbl 1480.93048
Benner, Peter; Köhler, Martin; Saak, Jens
2021
MORLAB – the model order reduction laboratory. Zbl 1480.93049
Benner, Peter; Werner, Steffen W. R.
2021
Frequency- and time-limited balanced truncation for large-scale second-order systems. Zbl 1467.93050
Benner, Peter; Werner, Steffen W. R.
2021
Structure-preserving interpolation of bilinear control systems. Zbl 1470.93032
Benner, Peter; Gugercin, Serkan; Werner, Steffen W. R.
2021
On error estimation for reduced-order modeling of linear non-parametric and parametric systems. Zbl 1480.37086
Feng, Lihong; Benner, Peter
2021
MathEnergy – mathematical key technologies for evolving energy grids. Zbl 1471.93045
Clees, Tanja; Baldin, Anton; Benner, Peter; Grundel, Sara; Himpe, Christian; Klaassen, Bernhard; Küsters, Ferdinand; Marheineke, Nicole; Nikitina, Lialia; Nikitin, Igor; Pade, Jonas; Stahl, Nadine; Strohm, Christian; Tischendorf, Caren; Wirsen, Andreas
2021
A low-rank approach for nonlinear parameter-dependent fluid-structure interaction problems. Zbl 1478.74024
Benner, Peter; Richter, Thomas; Weinhandl, Roman
2021
On the solution of the nonsymmetric T-Riccati equation. Zbl 1459.15015
Benner, Peter; Palitta, Davide
2021
Model order reduction for gas and energy networks. Zbl 1490.93021
Himpe, Christian; Grundel, Sara; Benner, Peter
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
Index-aware MOR for gas transport networks. Zbl 1428.93025
Banagaaya, Nicodemus; Grundel, Sara; Benner, Peter
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
Identification of port-Hamiltonian systems from frequency response data. Zbl 1451.93063
Benner, Peter; Goyal, Pawan; Van Dooren, Paul
2020
A subspace framework for $$\mathcal{H}_\infty$$-norm minimization. Zbl 1461.93123
Aliyev, Nicat; Benner, Peter; Mengi, Emre; Voigt, Matthias
2020
Efficient numerical methods for gas network modeling and simulation. Zbl 1457.76013
Qiu, Yue; Grundel, Sara; Stoll, Martin; Benner, Peter
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
Hankel-norm approximation of large-scale descriptor systems. Zbl 1441.93044
Benner, Peter; Werner, Steffen W. R.
2020
Optimal distributed and tangential boundary control for the unsteady stochastic Stokes equations. Zbl 1451.76045
Benner, Peter; Trautwein, Christoph
2020
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
Gas network benchmark models. Zbl 1445.76065
Benner, Peter; Grundel, Sara; Himpe, Christian; Huck, Christoph; Streubel, Tom; Tischendorf, Caren
2019
Extended and improved criss-cross algorithms for computing the spectral value set abscissa and radius. Zbl 1457.93066
Benner, Peter; Mitchell, Tim
2019
Cross-Gramian-based dominant subspaces. Zbl 1440.93043
Benner, Peter; Himpe, Christian
2019
Optimal control problems constrained by the stochastic Navier-Stokes equations with multiplicative Lévy noise. Zbl 1420.93036
Benner, Peter; Trautwein, Christoph
2019
A low-rank inexact Newton-Krylov method for stochastic eigenvalue problems. Zbl 1420.65043
Benner, Peter; Onwunta, Akwum; Stoll, Martin
2019
Periodic switching strategies for an isoperimetric control problem with application to nonlinear chemical reactions. Zbl 1461.49047
Benner, P.; Seidel-Morgenstern, A.; Zuyev, A.
2019
Greedy low-rank algorithm for spatial connectome regression. Zbl 1437.92005
Kürschner, Patrick; Dolgov, Sergey; Harris, Kameron Decker; Benner, Peter
2019
Index-preserving model order reduction for differential-algebraic systems arising in gas transport networks. Zbl 1469.76083
Banagaaya, Nicodemus; Benner, Peter; Grundel, Sara
2019
$$\mathcal H_2$$-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
Numerical solution of the infinite-dimensional LQR problem and the associated Riccati differential equations. Zbl 1444.65032
Benner, Peter; Mena, Hermann
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
Space-time Galerkin POD with application in optimal control of semilinear partial differential equations. Zbl 1392.35323
Baumann, Manuel; Benner, Peter; Heiland, Jan
2018
On reduced input-output dynamic mode decomposition. Zbl 1405.93051
Benner, Peter; Himpe, Christian; Mitchell, Tim
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
Faster and more accurate computation of the $$\mathcal{H}_\infty$$ norm via optimization. Zbl 1401.93087
Benner, Peter; Mitchell, Tim
2018
A linear quadratic control problem for the stochastic heat equation driven by Q-Wiener processes. Zbl 1370.93315
Benner, Peter; Trautwein, Christoph
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
Exponential stability and stabilization of extended linearizations via continuous updates of Riccati-based feedback. Zbl 1390.93655
Benner, P.; Heiland, J.
2018
Model reduction of linear multi-agent systems by clustering with $$\mathcal H_2$$ and $$\mathcal H_\infty$$ error bounds. Zbl 1395.93134
Jongsma, Hidde-Jan; Mlinarić, Petar; Grundel, Sara; Benner, Peter; Trentelman, Harry L.
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
A direct index 1 DAE model of gas networks. Zbl 1416.78021
Benner, Peter; Braukmüller, Maike; Grundel, Sara
2018
Optimal control of a Stefan problem fully coupled with incompressible Navier-Stokes equations and mesh movement. Zbl 1438.49050
Baran, Björn; Benner, Peter; Heiland, Jan; Saak, Jens
2018
Model reduction and approximation. Theory and algorithms. Zbl 1378.65010
2017
Model order reduction for differential-algebraic equations: a survey. Zbl 1402.93069
Benner, Peter; Stykel, Tatjana
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
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
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
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
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
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
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
Adaptive symmetric interior penalty Galerkin method for boundary control problems. Zbl 1362.65122
Benner, Peter; Yücel, Hamdullah
2017
Structure preserving iterative methods for periodic projected Lyapunov equations and their application in model reduction of periodic descriptor systems. Zbl 1377.93053
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
Reduced basis approximations for Maxwell’s equations in dispersive media. Zbl 1388.78018
Benner, Peter; Hess, Martin
2017
System reduction for nanoscale IC design. Zbl 1367.65003
2017
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
On the solution of large-scale algebraic Riccati equations by using low-dimensional invariant subspaces. Zbl 1330.15017
Benner, Peter; Bujanović, Zvonimir
2016
Frequency-limited balanced truncation with low-rank approximations. Zbl 1391.65123
Benner, Peter; Kürschner, Patrick; Saak, Jens
2016
Block-diagonal preconditioning for optimal control problems constrained by PDEs with uncertain inputs. Zbl 1382.65074
Benner, Peter; Onwunta, Akwum; Stoll, Martin
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
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
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
Low-rank Newton-ADI methods for large nonsymmetric algebraic Riccati equations. Zbl 1336.93056
Benner, Peter; Kürschner, Patrick; Saak, Jens
2016
Positive operators and stable truncation. Zbl 1335.15016
Benner, Peter; Damm, Tobias; Redmann, Martin; Rodriguez Cruz, Yolanda Rocio
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
Two-sided projection methods for nonlinear model order reduction. Zbl 1312.93016
Benner, Peter; Breiten, Tobias
2015
Model reduction for stochastic systems. Zbl 1331.65017
Benner, Peter; Redmann, Martin
2015
Low-rank solution of unsteady diffusion equations with stochastic coefficients. Zbl 1325.65016
Benner, Peter; Onwunta, Akwum; Stoll, Martin
2015
Recycling BiCGSTAB with an application to parametric model order reduction. Zbl 1325.65044
Ahuja, Kapil; Benner, Peter; de Sturler, Eric; Feng, Lihong
2015
Riccati-based boundary feedback stabilization of incompressible Navier-Stokes flows. Zbl 1312.93083
Bänsch, Eberhard; Benner, Peter; Saak, Jens; Weichelt, Heiko K.
2015
Numerical linear algebra methods for linear differential-algebraic equations. Zbl 1343.65100
Benner, Peter; Losse, Philip; Mehrmann, Volker; Voigt, Matthias
2015
LQG-balanced truncation low-order controller for stabilization of laminar flows. Zbl 1308.76105
Benner, Peter; Heiland, Jan
2015
Model order reduction for coupled problems (survey). Zbl 1455.74003
Benner, Peter; Feng, Lihong
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
Numerical algebra, matrix theory, differential-algebraic equations and control theory. Festschrift in honor of Volker Mehrmann. Zbl 1322.00048
2015
Adaptive discontinuous Galerkin methods for state constrained optimal control problems governed by convection diffusion equations. Zbl 1333.49047
Yücel, Hamdullah; 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
Parametric model order reduction of thermal models using the bilinear interpolatory rational Krylov algorithm. Zbl 1310.93038
Bruns, Angelika; 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
...and 121 more Documents
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### Cited by 1,685 Authors

 151 Benner, Peter 31 Gugercin, Serkan 31 Jiang, Yaolin 31 Mehrmann, Volker 20 Saak, Jens 19 Kressner, Daniel 19 Peherstorfer, Benjamin 19 Redmann, Martin 19 Stoll, Martin 19 Stykel, Tatjana 18 Feng, Lihong 18 Kürschner, Patrick 18 Simoncini, Valeria 17 Breiten, Tobias 16 Beattie, Christopher A. 16 Willcox, Karen E. 15 Faßbender, Heike 15 Rozza, Gianluigi 13 Kutz, J. Nathan 13 Mena, Hermann 13 Quintana-Ortí, Enrique S. 12 Brunton, Steven L. 12 Jbilou, Khalide 12 Pulch, Roland 11 Dolgov, Sergey V. 11 Eberhard, Peter 11 Goyal, Pawan 11 Grundel, Sara M. 11 Khoromskiĭ, Boris Nikolaevich 10 Antoulas, Athanasios C. 10 Gosea, Ion Victor 10 Haasdonk, Bernard 10 King-wah Chu, Eric 10 Tomljanović, Zoran 10 Voigt, Matthias 9 Hesthaven, Jan S. 9 Lin, Wen-Wei 9 Truhar, Ninoslav 9 Xu, Hongguo 8 de Sturler, Eric 8 Fan, Hung-Yuan 8 Heiland, Jan 8 Krämer, Boris 8 Ma, Changfeng 8 Manzoni, Andrea 8 Palitta, Davide 8 Van Dooren, Paul M. 8 Watkins, David S. 8 Xu, Kangli 7 Ahmad, Mian Ilyas 7 Alla, Alessandro 7 Hajarian, Masoud 7 Heinkenschloss, Matthias 7 Himpe, Christian 7 Lohmann, Boris 7 Mehl, Christian 7 Poloni, Federico G. 7 Pontes Duff, Igor 7 Quarteroni, Alfio M. 7 Singler, John R. 7 Wang, Xiaolong 7 Xiao, Zhihua 7 Yadykin, Igor B. 6 Ballarin, Francesco 6 Baur, Ulrike 6 Chen, Xiaoshan 6 Fehr, Jörg 6 Freitag, Melina A. 6 Jarlebring, Elias 6 Karasözen, Bülent 6 Khoromskaia, Venera 6 Kunisch, Karl 6 Li, Rencang 6 Marheineke, Nicole 6 Mitchell, Tim 6 Narayan, Akil C. 6 Reis, Timo 6 Robol, Leonardo 6 Uddin, Mohammad Monir 6 Unger, Benjamin 6 Uzunca, Murat 6 Werner, Steffen W. R. 6 Yücel, Hamdullah 6 Zimmermann, Ralf 5 Banagaaya, Nicodemus 5 Bentbib, Abdeslem Hafid 5 Chen, Peng 5 Damm, Tobias 5 Dehghan Takht Fooladi, Mehdi 5 Desmet, Wim 5 Drmač, Zlatko 5 Elman, Howard C. 5 Hartmann, Carsten 5 Huang, Ting-Zhu 5 Lee, Kookjin 5 Meerbergen, Karl 5 Mengi, Emre 5 Nouy, Anthony 5 Quintana-Ortí, Gregorio 5 Schulze, Philipp ...and 1,585 more Authors
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### Cited in 187 Serials

 90 SIAM Journal on Scientific Computing 81 Linear Algebra and its Applications 54 Journal of Computational and Applied Mathematics 51 Computer Methods in Applied Mechanics and Engineering 48 Journal of Computational Physics 46 SIAM Journal on Matrix Analysis and Applications 37 Advances in Computational Mathematics 34 Applied Mathematics and Computation 28 Journal of the Franklin Institute 27 Journal of Scientific Computing 24 Systems & Control Letters 24 Applied Numerical Mathematics 24 Numerical Algorithms 22 International Journal of Control 21 Numerical Linear Algebra with Applications 20 Computers & Mathematics with Applications 20 SIAM/ASA Journal on Uncertainty Quantification 19 BIT 19 Mathematical and Computer Modelling of Dynamical Systems 16 Automatica 16 Numerische Mathematik 16 SIAM Journal on Control and Optimization 12 ETNA. Electronic Transactions on Numerical Analysis 10 Applied Mathematical Modelling 10 International Journal of Computer Mathematics 10 Computational and Applied Mathematics 10 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 10 Numerical Algebra, Control and Optimization 10 International Journal of Systems Science. Principles and Applications of Systems and Integration 9 Mathematics of Computation 9 Applied Mathematics Letters 8 Computers and Fluids 8 Computational Mechanics 8 Mathematical Problems in Engineering 8 Vietnam Journal of Mathematics 7 Mathematics and Computers in Simulation 7 Automation and Remote Control 6 Linear and Multilinear Algebra 6 MCSS. Mathematics of Control, Signals, and Systems 5 Journal of Fluid Mechanics 5 International Journal for Numerical Methods in Engineering 5 SIAM Journal on Numerical Analysis 5 SIAM Review 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 5 SIAM Journal on Applied Dynamical Systems 5 Advances in Difference Equations 4 Computational Optimization and Applications 4 Doklady Mathematics 4 Multiscale Modeling & Simulation 4 GAMM-Mitteilungen 4 Communications in Computational Physics 4 Algorithms 4 Journal of Mathematics in Industry 3 Journal of Mathematical Analysis and Applications 3 Applied Mathematics and Optimization 3 Calcolo 3 Physica D 3 SIAM Journal on Optimization 3 European Journal of Control 3 Computing and Visualization in Science 3 Journal of Numerical Mathematics 3 Journal of Applied Mathematics and Computing 3 Journal of Industrial and Management Optimization 3 Asian Journal of Control 3 Mathematical Control and Related Fields 3 Journal of Computational Dynamics 3 East Asian Journal on Applied Mathematics 3 Journal of Mathematical Modeling 3 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 2 International Journal of Systems Science 2 Inverse Problems 2 Journal of Engineering Mathematics 2 ACM Transactions on Mathematical Software 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 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 2 Journal of Nonlinear Science 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 International Journal of Computational Methods 2 Acta Numerica 2 International Journal of Numerical Analysis and Modeling 2 Complex Analysis and Operator Theory 2 Frontiers of Mathematics in China 2 Nonlinear Analysis. Hybrid Systems ...and 87 more Serials
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### Cited in 52 Fields

 783 Numerical analysis (65-XX) 417 Systems theory; control (93-XX) 308 Linear and multilinear algebra; matrix theory (15-XX) 182 Partial differential equations (35-XX) 129 Calculus of variations and optimal control; optimization (49-XX) 128 Fluid mechanics (76-XX) 67 Dynamical systems and ergodic theory (37-XX) 57 Ordinary differential equations (34-XX) 54 Mechanics of deformable solids (74-XX) 51 Probability theory and stochastic processes (60-XX) 47 Operations research, mathematical programming (90-XX) 45 Computer science (68-XX) 39 Statistics (62-XX) 35 Optics, electromagnetic theory (78-XX) 32 Operator theory (47-XX) 32 Mechanics of particles and systems (70-XX) 31 Approximations and expansions (41-XX) 24 Biology and other natural sciences (92-XX) 16 Classical thermodynamics, heat transfer (80-XX) 13 Statistical mechanics, structure of matter (82-XX) 13 Information and communication theory, circuits (94-XX) 9 Functions of a complex variable (30-XX) 9 Geophysics (86-XX) 8 Functional analysis (46-XX) 7 Combinatorics (05-XX) 6 Special functions (33-XX) 5 Differential geometry (53-XX) 5 Quantum theory (81-XX) 4 General and overarching topics; collections (00-XX) 4 History and biography (01-XX) 4 Algebraic geometry (14-XX) 4 Group theory and generalizations (20-XX) 4 Difference and functional equations (39-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 2 Number theory (11-XX) 2 Real functions (26-XX) 2 Algebraic topology (55-XX) 2 Global analysis, analysis on manifolds (58-XX) 1 Field theory and polynomials (12-XX) 1 Commutative algebra (13-XX) 1 Associative rings and algebras (16-XX) 1 Nonassociative rings and algebras (17-XX) 1 Category theory; homological algebra (18-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 General topology (54-XX)

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