Edit Profile (opens in new tab) Breiten, Tobias Co-Author Distance Author ID: breiten.tobias Published as: Breiten, Tobias; Breiten, T. Homepage: http://imsc.uni-graz.at/breiten/ External Links: MGP · GND Documents Indexed: 43 Publications since 2010, including 1 Book and 5 Additional arXiv Preprints 1 Contribution as Editor Reviewing Activity: 8 Reviews Co-Authors: 30 Co-Authors with 42 Joint Publications 862 Co-Co-Authors all top 5 Co-Authors 2 single-authored 13 Kunisch, Karl 10 Benner, Peter 6 Pfeiffer, Laurent 3 Stoll, Martin 2 Beattie, Christopher A. 2 Damm, Tobias 2 Gugercin, Serkan 2 Hartmann, Carsten 2 Schröder, Jesper 2 Schulze, Philipp 2 Stykel, Tatjana 2 Unger, Benjamin 1 Borghi, Alessandro 1 Dolgov, Sergey V. 1 Faßbender, Heike 1 Feng, Lihong 1 Hinsen, Dorothea 1 Hinze, Michael 1 Höveler, Bernhard 1 Karsai, Attila 1 Morandin, Riccardo 1 Neureither, Lara 1 Puche, Marc 1 Reis, Timo 1 Ringh, Emil 1 Rodrigues, Sérgio S. 1 Schmidt, Burkhard 1 Sharma, Upanshu 1 Simoncini, Valeria 1 Zimmermann, Ralf all top 5 Serials 7 SIAM Journal on Control and Optimization 5 Systems & Control Letters 2 SIAM Journal on Scientific Computing 2 ETNA. Electronic Transactions on Numerical Analysis 2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 2 Mathematical Control and Related Fields 1 Computers & Mathematics with Applications 1 International Journal of Control 1 Journal of Mathematical Physics 1 Applied Mathematics and Optimization 1 Automatica 1 BIT 1 Journal of Differential Equations 1 Numerische Mathematik 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 SIAM Journal on Matrix Analysis and Applications 1 Discrete and Continuous Dynamical Systems 1 ISNM. International Series of Numerical Mathematics 1 Numerical Algebra, Control and Optimization 1 Journal of Computational Dynamics all top 5 Fields 36 Systems theory; control (93-XX) 11 Calculus of variations and optimal control; optimization (49-XX) 11 Numerical analysis (65-XX) 10 Partial differential equations (35-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 Ordinary differential equations (34-XX) 2 Operator theory (47-XX) 2 Fluid mechanics (76-XX) 2 Biology and other natural sciences (92-XX) 1 General and overarching topics; collections (00-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Probability theory and stochastic processes (60-XX) 1 Mechanics of deformable solids (74-XX) 1 Optics, electromagnetic theory (78-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 34 Publications have been cited 481 times in 326 Documents Cited by ▼ Year ▼ Interpolation-based \({\mathcal H}_2\)-model reduction of bilinear control systems. Zbl 1256.93027 Benner, Peter; Breiten, Tobias 64 2012 Krylov subspace methods for model order reduction of bilinear control systems. Zbl 1198.93055 Breiten, Tobias; Damm, Tobias 49 2010 Low rank methods for a class of generalized Lyapunov equations and related issues. Zbl 1266.65068 Benner, Peter; Breiten, Tobias 45 2013 A low-rank in time approach to PDE-constrained optimization. Zbl 1330.65153 Stoll, Martin; Breiten, Tobias 40 2015 Two-sided projection methods for nonlinear model order reduction. Zbl 1312.93016 Benner, Peter; Breiten, Tobias 40 2015 Low-rank solvers for fractional differential equations. Zbl 1338.65071 Breiten, Tobias; Simoncini, Valeria; Stoll, Martin 37 2016 Riccati-based feedback control of the monodomain equations with the Fitzhugh-Nagumo model. Zbl 1316.93047 Breiten, Tobias; Kunisch, Karl 23 2015 Generalised tangential interpolation for model reduction of discrete-time MIMO bilinear systems. Zbl 1230.93010 Benner, P.; Breiten, T.; Damm, T. 17 2011 Krylov-subspace based model reduction of nonlinear circuit models using bilinear and quadratic-linear approximations. Zbl 1246.78035 Benner, Peter; Breiten, Tobias 16 2012 Feedback stabilization to nonstationary solutions of a class of reaction diffusion equations of Fitzhugh-Nagumo type. Zbl 1370.35176 Breiten, Tobias; Kunisch, Karl; Rodrigues, Sérgio S. 15 2017 On the turnpike property and the receding-horizon method for linear-quadratic optimal control problems. Zbl 1437.49047 Breiten, Tobias; Pfeiffer, Laurent 15 2020 Control strategies for the Fokker-Planck equation. Zbl 1403.35298 Breiten, Tobias; Kunisch, Karl; Pfeiffer, Laurent 13 2018 Infinite-horizon bilinear optimal control problems: sensitivity analysis and polynomial feedback laws. Zbl 1401.49004 Breiten, Tobias; Kunisch, Karl; Pfeiffer, Laurent 12 2018 Structure-preserving model reduction for integro-differential equations. Zbl 1350.93025 Breiten, Tobias 10 2016 Near-optimal frequency-weighted interpolatory model reduction. Zbl 1320.93028 Breiten, Tobias; Beattie, Christopher; Gugercin, Serkan 10 2015 On optimality of approximate low rank solutions of large-scale matrix equations. Zbl 1292.65040 Benner, Peter; Breiten, Tobias 9 2014 Compensator design for the monodomain equations with the FitzHugh-Nagumo model. Zbl 1371.35153 Breiten, Tobias; Kunisch, Karl 8 2017 Feedback stabilization of the two-dimensional Navier-Stokes equations by value function approximation. Zbl 1425.35135 Breiten, Tobias; Kunisch, Karl; Pfeiffer, Laurent 8 2019 Taylor expansions of the value function associated with a bilinear optimal control problem. Zbl 1420.49005 Breiten, Tobias; Kunisch, Karl; Pfeiffer, Laurent 8 2019 Funnel control for the monodomain equations with the FitzHugh-Nagumo model. Zbl 1462.35174 Berger, Thomas; Breiten, Tobias; Puche, Marc; Reis, Timo 7 2021 Numerical study of polynomial feedback laws for a bilinear control problem. Zbl 1418.49002 Breiten, Tobias; Kunisch, Karl; Pfeiffer, Laurent 6 2018 Interpolatory methods for model reduction of large-scale dynamical systems. Zbl 1283.93003 Breiten, Tobias 5 2013 Passivity preserving model reduction via spectral factorization. Zbl 1494.93024 Breiten, Tobias; Unger, Benjamin 5 2022 Solving differential Riccati equations: a nonlinear space-time method using tensor trains. Zbl 1479.49070 Breiten, Tobias; Dolgov, Sergey; Stoll, Martin 4 2021 Error bounds for port-Hamiltonian model and controller reduction based on system balancing. Zbl 1524.93007 Breiten, Tobias; Morandin, Riccardo; Schulze, Philipp 4 2022 Balancing-related model reduction methods. Zbl 1505.93028 Breiten, Tobias; Stykel, Tatjana 2 2021 Feedback stabilization of the three-dimensional Navier-Stokes equations using generalized Lyapunov equations. Zbl 1434.35086 Breiten, Tobias; Kunisch, Karl 2 2020 Matrix equations and model reduction. Zbl 1332.65083 Benner, Peter; Breiten, Tobias; Feng, Lihong 1 2015 Rational interpolation methods for symmetric Sylvester equations. Zbl 1312.65067 Benner, Peter; Breiten, Tobias 1 2014 Boundary feedback stabilization of the monodomain equations. Zbl 1366.35081 Breiten, Tobias; Kunisch, Karl 1 2017 Neural network based nonlinear observers. Zbl 1478.93220 Breiten, Tobias; Kunisch, Karl 1 2021 Stochastic gradient descent and fast relaxation to thermodynamic equilibrium: a stochastic control approach. Zbl 1491.82014 Breiten, Tobias; Hartmann, Carsten; Neureither, Lara; Sharma, Upanshu 1 2021 Residual-based iterations for the generalized Lyapunov equation. Zbl 1507.65073 Breiten, Tobias; Ringh, Emil 1 2019 Model reduction of controlled Fokker-Planck and Liouville-von Neumann equations. Zbl 1448.93039 Benner, Peter; Breiten, Tobias; Hartmann, Carsten; Schmidt, Burkhard 1 2020 Passivity preserving model reduction via spectral factorization. Zbl 1494.93024 Breiten, Tobias; Unger, Benjamin 5 2022 Error bounds for port-Hamiltonian model and controller reduction based on system balancing. Zbl 1524.93007 Breiten, Tobias; Morandin, Riccardo; Schulze, Philipp 4 2022 Funnel control for the monodomain equations with the FitzHugh-Nagumo model. Zbl 1462.35174 Berger, Thomas; Breiten, Tobias; Puche, Marc; Reis, Timo 7 2021 Solving differential Riccati equations: a nonlinear space-time method using tensor trains. Zbl 1479.49070 Breiten, Tobias; Dolgov, Sergey; Stoll, Martin 4 2021 Balancing-related model reduction methods. Zbl 1505.93028 Breiten, Tobias; Stykel, Tatjana 2 2021 Neural network based nonlinear observers. Zbl 1478.93220 Breiten, Tobias; Kunisch, Karl 1 2021 Stochastic gradient descent and fast relaxation to thermodynamic equilibrium: a stochastic control approach. Zbl 1491.82014 Breiten, Tobias; Hartmann, Carsten; Neureither, Lara; Sharma, Upanshu 1 2021 On the turnpike property and the receding-horizon method for linear-quadratic optimal control problems. Zbl 1437.49047 Breiten, Tobias; Pfeiffer, Laurent 15 2020 Feedback stabilization of the three-dimensional Navier-Stokes equations using generalized Lyapunov equations. Zbl 1434.35086 Breiten, Tobias; Kunisch, Karl 2 2020 Model reduction of controlled Fokker-Planck and Liouville-von Neumann equations. Zbl 1448.93039 Benner, Peter; Breiten, Tobias; Hartmann, Carsten; Schmidt, Burkhard 1 2020 Feedback stabilization of the two-dimensional Navier-Stokes equations by value function approximation. Zbl 1425.35135 Breiten, Tobias; Kunisch, Karl; Pfeiffer, Laurent 8 2019 Taylor expansions of the value function associated with a bilinear optimal control problem. Zbl 1420.49005 Breiten, Tobias; Kunisch, Karl; Pfeiffer, Laurent 8 2019 Residual-based iterations for the generalized Lyapunov equation. Zbl 1507.65073 Breiten, Tobias; Ringh, Emil 1 2019 Control strategies for the Fokker-Planck equation. Zbl 1403.35298 Breiten, Tobias; Kunisch, Karl; Pfeiffer, Laurent 13 2018 Infinite-horizon bilinear optimal control problems: sensitivity analysis and polynomial feedback laws. Zbl 1401.49004 Breiten, Tobias; Kunisch, Karl; Pfeiffer, Laurent 12 2018 Numerical study of polynomial feedback laws for a bilinear control problem. Zbl 1418.49002 Breiten, Tobias; Kunisch, Karl; Pfeiffer, Laurent 6 2018 Feedback stabilization to nonstationary solutions of a class of reaction diffusion equations of Fitzhugh-Nagumo type. Zbl 1370.35176 Breiten, Tobias; Kunisch, Karl; Rodrigues, Sérgio S. 15 2017 Compensator design for the monodomain equations with the FitzHugh-Nagumo model. Zbl 1371.35153 Breiten, Tobias; Kunisch, Karl 8 2017 Boundary feedback stabilization of the monodomain equations. Zbl 1366.35081 Breiten, Tobias; Kunisch, Karl 1 2017 Low-rank solvers for fractional differential equations. Zbl 1338.65071 Breiten, Tobias; Simoncini, Valeria; Stoll, Martin 37 2016 Structure-preserving model reduction for integro-differential equations. Zbl 1350.93025 Breiten, Tobias 10 2016 A low-rank in time approach to PDE-constrained optimization. Zbl 1330.65153 Stoll, Martin; Breiten, Tobias 40 2015 Two-sided projection methods for nonlinear model order reduction. Zbl 1312.93016 Benner, Peter; Breiten, Tobias 40 2015 Riccati-based feedback control of the monodomain equations with the Fitzhugh-Nagumo model. Zbl 1316.93047 Breiten, Tobias; Kunisch, Karl 23 2015 Near-optimal frequency-weighted interpolatory model reduction. Zbl 1320.93028 Breiten, Tobias; Beattie, Christopher; Gugercin, Serkan 10 2015 Matrix equations and model reduction. Zbl 1332.65083 Benner, Peter; Breiten, Tobias; Feng, Lihong 1 2015 On optimality of approximate low rank solutions of large-scale matrix equations. Zbl 1292.65040 Benner, Peter; Breiten, Tobias 9 2014 Rational interpolation methods for symmetric Sylvester equations. Zbl 1312.65067 Benner, Peter; Breiten, Tobias 1 2014 Low rank methods for a class of generalized Lyapunov equations and related issues. Zbl 1266.65068 Benner, Peter; Breiten, Tobias 45 2013 Interpolatory methods for model reduction of large-scale dynamical systems. Zbl 1283.93003 Breiten, Tobias 5 2013 Interpolation-based \({\mathcal H}_2\)-model reduction of bilinear control systems. Zbl 1256.93027 Benner, Peter; Breiten, Tobias 64 2012 Krylov-subspace based model reduction of nonlinear circuit models using bilinear and quadratic-linear approximations. Zbl 1246.78035 Benner, Peter; Breiten, Tobias 16 2012 Generalised tangential interpolation for model reduction of discrete-time MIMO bilinear systems. Zbl 1230.93010 Benner, P.; Breiten, T.; Damm, T. 17 2011 Krylov subspace methods for model order reduction of bilinear control systems. Zbl 1198.93055 Breiten, Tobias; Damm, Tobias 49 2010 all cited Publications top 5 cited Publications all top 5 Cited by 415 Authors 39 Benner, Peter 26 Kunisch, Karl 23 Breiten, Tobias 23 Jiang, Yaolin 16 Gugercin, Serkan 12 Redmann, Martin 12 Stoll, Martin 11 Goyal, Pawan 9 Simoncini, Valeria 8 Ahmad, Mian Ilyas 8 Palitta, Davide 8 Rodrigues, Sérgio S. 8 Willcox, Karen E. 8 Xu, Kangli 7 Dolgov, Sergey V. 6 Beattie, Christopher A. 6 Gosea, Ion Victor 6 Maksimov, Vyacheslav Ivanovich 6 Pfeiffer, Laurent 6 Wang, Xiaolong 5 Azmi, Behzad 5 Chen, Hao 5 Krämer, Boris 5 Lei, Siulong 5 Pontes Duff, Igor 5 Xiao, Zhihua 4 Feng, Lihong 4 Kalise, Dante 4 Karasözen, Bülent 4 Kürschner, Patrick 4 Liang, Zhaozheng 4 Onwunta, Akwum 4 Peherstorfer, Benjamin 4 Pulch, Roland 4 Uzunca, Murat 4 Yücel, Hamdullah 3 Antoulas, Athanasios C. 3 Cao, Xingang 3 Casas, Eduardo 3 Chou, Lot-Kei 3 Damm, Tobias 3 Du, Xin 3 Grüne, Lars 3 Haasdonk, Bernard 3 Hackbusch, Wolfgang 3 Hartmann, Carsten 3 Li, Zhen 3 Lü, Wen 3 Massei, Stefano 3 Pearson, John W. 3 Qi, Zhen-Zhong 3 Qian, Elizabeth 3 Robol, Leonardo 3 Saak, Jens 3 Schilders, Wil H. A. 3 Schwenninger, Felix L. 3 Song, Qiu-Yan 3 Sreeram, Victor 3 Szyld, Daniel B. 3 Tröltzsch, Fredi 3 Wang, Hong 3 Werner, Steffen W. R. 3 Yıldız, Süleyman 3 Zhang, Guofeng 3 Zulfiqar, Umair 2 Alla, Alessandro 2 Baur, Ulrike 2 Becker, Simon 2 Biros, George 2 Bünger, Alexandra 2 Çiloğlu, Pelin 2 Cordoni, Francesco Giuseppe 2 Court, Sébastien 2 Dehghan Takht Fooladi, Mehdi 2 Di Persio, Luca 2 Diaz, Alejandro N. 2 Drmač, Zlatko 2 Eghtesad, Mohammad 2 Elman, Howard C. 2 Fan, Hung-Yuan 2 Fleig, Arthur 2 Freitag, Melina A. 2 Grafke, Tobias 2 Grauer, Rainer 2 Grundel, Sara M. 2 Heiland, Jan 2 Heinkenschloss, Matthias 2 Hesthaven, Jan S. 2 Hinze, Michael 2 Holtmannspötter, Marita 2 Hou, Liangshao 2 Huang, Qiuyue 2 Huang, Yun-Chi 2 King-wah Chu, Eric 2 Kressner, Daniel 2 Lee, Kookjin 2 Liljegren-Sailer, Björn 2 Lohmann, Boris 2 Mahmoodi, Masih 2 Mang, Andreas ...and 315 more Authors all top 5 Cited in 94 Serials 22 SIAM Journal on Scientific Computing 15 SIAM Journal on Control and Optimization 14 Journal of the Franklin Institute 11 SIAM Journal on Matrix Analysis and Applications 10 Advances in Computational Mathematics 9 International Journal of Control 9 Applied Mathematics and Computation 8 Computers & Mathematics with Applications 8 Journal of Computational and Applied Mathematics 8 Systems & Control Letters 8 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 8 International Journal of Systems Science. Principles and Applications of Systems and Integration 6 BIT 6 Linear Algebra and its Applications 6 Evolution Equations and Control Theory 5 Computer Methods in Applied Mechanics and Engineering 5 Journal of Computational Physics 5 Applied Mathematics and Optimization 5 Automatica 5 Journal of Scientific Computing 5 Mathematical and Computer Modelling of Dynamical Systems 5 Mathematical Control and Related Fields 4 Mathematics and Computers in Simulation 4 Applied Numerical Mathematics 4 MCSS. Mathematics of Control, Signals, and Systems 4 Numerical Algorithms 4 Applied Mathematical Modelling 4 Discrete and Continuous Dynamical Systems 4 Vietnam Journal of Mathematics 4 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 4 Acta Numerica 3 Journal of Differential Equations 3 International Journal of Computer Mathematics 3 Oberwolfach Reports 3 GAMM-Mitteilungen 3 SIAM/ASA Journal on Uncertainty Quantification 2 Calcolo 2 Numerische Mathematik 2 SIAM Journal on Numerical Analysis 2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 2 Computational Mechanics 2 Numerical Methods for Partial Differential Equations 2 SIAM Review 2 Computational and Applied Mathematics 2 European Journal of Control 2 Differential Equations 2 SIAM Journal on Applied Dynamical Systems 2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 2 Numerical Algebra, Control and Optimization 2 Journal of Computational Dynamics 2 AIMS Mathematics 2 Electronic Research Archive 1 Computer Physics Communications 1 Journal of Mathematical Analysis and Applications 1 Journal of Statistical Physics 1 Chaos, Solitons and Fractals 1 Canadian Mathematical Bulletin 1 International Journal for Numerical Methods in Engineering 1 Journal of Pure and Applied Algebra 1 Chinese Annals of Mathematics. Series B 1 Physica D 1 Applied Mathematics Letters 1 Neural Networks 1 Computational Mathematics and Mathematical Physics 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 SIAM Journal on Mathematical Analysis 1 International Journal of Robust and Nonlinear Control 1 Numerical Linear Algebra with Applications 1 Journal of Inverse and Ill-Posed Problems 1 ETNA. Electronic Transactions on Numerical Analysis 1 Applied Mathematical Finance 1 Journal of Difference Equations and Applications 1 Electronic Journal of Probability 1 Computing and Visualization in Science 1 Multibody System Dynamics 1 Soft Computing 1 Discrete Dynamics in Nature and Society 1 International Journal of Applied Mathematics and Computer Science 1 Computational Geosciences 1 Archives of Computational Methods in Engineering 1 Journal of Systems Science and Complexity 1 Computational Methods in Applied Mathematics 1 Journal of Machine Learning Research (JMLR) 1 Bulletin of the Brazilian Mathematical Society. New Series 1 Proceedings of the Steklov Institute of Mathematics 1 Journal of Physics A: Mathematical and Theoretical 1 Networks and Heterogeneous Media 1 Numerical Mathematics: Theory, Methods and Applications 1 SIAM Journal on Financial Mathematics 1 The Journal of Mathematical Neuroscience 1 Journal of Mathematical Modeling 1 Modern Stochastics. Theory and Applications 1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys 1 Results in Applied Mathematics all top 5 Cited in 35 Fields 171 Systems theory; control (93-XX) 148 Numerical analysis (65-XX) 92 Partial differential equations (35-XX) 68 Calculus of variations and optimal control; optimization (49-XX) 49 Linear and multilinear algebra; matrix theory (15-XX) 25 Probability theory and stochastic processes (60-XX) 17 Ordinary differential equations (34-XX) 17 Fluid mechanics (76-XX) 13 Approximations and expansions (41-XX) 12 Dynamical systems and ergodic theory (37-XX) 12 Operations research, mathematical programming (90-XX) 9 Computer science (68-XX) 8 Operator theory (47-XX) 8 Mechanics of deformable solids (74-XX) 7 Biology and other natural sciences (92-XX) 6 Statistics (62-XX) 5 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 General and overarching topics; collections (00-XX) 3 Real functions (26-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Optics, electromagnetic theory (78-XX) 3 Geophysics (86-XX) 3 Information and communication theory, circuits (94-XX) 2 Functions of a complex variable (30-XX) 2 Differential geometry (53-XX) 2 Mechanics of particles and systems (70-XX) 2 Quantum theory (81-XX) 1 Commutative algebra (13-XX) 1 Algebraic geometry (14-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Sequences, series, summability (40-XX) 1 Integral equations (45-XX) 1 Functional analysis (46-XX) 1 General topology (54-XX) Citations by Year