Kapadia, Harshit; Feng, Lihong; Benner, Peter Active-learning-driven surrogate modeling for efficient simulation of parametric nonlinear systems. (English) Zbl 07796680 Comput. Methods Appl. Mech. Eng. 419, Article ID 116657, 36 p. (2024). MSC: 76-XX 92-XX PDFBibTeX XMLCite \textit{H. Kapadia} et al., Comput. Methods Appl. Mech. Eng. 419, Article ID 116657, 36 p. (2024; Zbl 07796680) Full Text: DOI arXiv
Benner, Peter; Nakatsukasa, Yuji; Penke, Carolin A structure-preserving divide-and-conquer method for pseudosymmetric matrices. (English) Zbl 07737638 SIAM J. Matrix Anal. Appl. 44, No. 3, 1245-1270 (2023). MSC: 65Fxx PDFBibTeX XMLCite \textit{P. Benner} et al., SIAM J. Matrix Anal. Appl. 44, No. 3, 1245--1270 (2023; Zbl 07737638) Full Text: DOI arXiv
Benner, Peter; Heiland, Jan; Werner, Steffen W. R. A low-rank solution method for Riccati equations with indefinite quadratic terms. (English) Zbl 1506.65063 Numer. Algorithms 92, No. 2, 1083-1103 (2023). MSC: 65F45 65F50 PDFBibTeX XMLCite \textit{P. Benner} et al., Numer. Algorithms 92, No. 2, 1083--1103 (2023; Zbl 1506.65063) Full Text: DOI arXiv
Benner, Peter; Palitta, Davide; Saak, Jens On an integrated Krylov-ADI solver for large-scale Lyapunov equations. (English) Zbl 07644383 Numer. Algorithms 92, No. 1, 35-63 (2023). MSC: 65-XX 15A24 65F10 65F30 15A06 PDFBibTeX XMLCite \textit{P. Benner} et al., Numer. Algorithms 92, No. 1, 35--63 (2023; Zbl 07644383) Full Text: DOI arXiv
Chellappa, Sridhar; Feng, Lihong; Benner, Peter An adaptive sampling approach for the reduced basis method. (English) Zbl 1504.93036 Beattie, Christopher (ed.) et al., Realization and model reduction of dynamical systems. A festschrift in honor of the 70th birthday of Thanos Antoulas. Cham: Springer. 137-155 (2022). MSC: 93B11 93C40 65D12 PDFBibTeX XMLCite \textit{S. Chellappa} et al., in: Realization and model reduction of dynamical systems. A festschrift in honor of the 70th birthday of Thanos Antoulas. Cham: Springer. 137--155 (2022; Zbl 1504.93036) Full Text: DOI arXiv
Banagaaya, Nicodemus; Alì, Giuseppe; Grundel, Sara; Benner, Peter Index-aware model-order reduction for a special class of nonlinear differential-algebraic equations. (English) Zbl 1519.93041 J. Dyn. Differ. Equations 34, No. 3, 2465-2489 (2022). MSC: 93B11 93C10 93C15 34A09 34A34 76N15 PDFBibTeX XMLCite \textit{N. Banagaaya} et al., J. Dyn. Differ. Equations 34, No. 3, 2465--2489 (2022; Zbl 1519.93041) Full Text: DOI arXiv
Cherifi, Karim; Goyal, Pawan; Benner, Peter A non-intrusive method to inferring linear port-Hamiltonian realizations using time-domain data. (English) Zbl 1492.93037 ETNA, Electron. Trans. Numer. Anal. 56, 102-116 (2022). MSC: 93B30 93B70 93B15 93C80 PDFBibTeX XMLCite \textit{K. Cherifi} et al., ETNA, Electron. Trans. Numer. Anal. 56, 102--116 (2022; Zbl 1492.93037) Full Text: DOI arXiv Link
Benner, Peter; Goyal, Pawan; Heiland, Jan; Duff, Igor Pontes Operator inference and physics-informed learning of low-dimensional models for incompressible flows. (English) Zbl 1505.76072 ETNA, Electron. Trans. Numer. Anal. 56, 28-51 (2022). MSC: 76M99 76D05 76D25 68T05 PDFBibTeX XMLCite \textit{P. Benner} et al., ETNA, Electron. Trans. Numer. Anal. 56, 28--51 (2022; Zbl 1505.76072) Full Text: DOI arXiv
Benner, Peter; Heiland, Jan; Werner, Steffen W. R. Robust output-feedback stabilization for incompressible flows using low-dimensional \(\mathcal{H}_{\infty}\)-controllers. (English) Zbl 1490.93102 Comput. Optim. Appl. 82, No. 1, 225-249 (2022). MSC: 93D15 93B36 93C20 35Q30 76D55 PDFBibTeX XMLCite \textit{P. Benner} et al., Comput. Optim. Appl. 82, No. 1, 225--249 (2022; Zbl 1490.93102) Full Text: DOI arXiv
Himpe, Christian; Grundel, Sara; Benner, Peter Model order reduction for gas and energy networks. (English) Zbl 1490.93021 J. Math. Ind. 11, Paper No. 13, 46 p. (2021). MSC: 93B11 93B70 93C20 93-04 76N15 PDFBibTeX XMLCite \textit{C. Himpe} et al., J. Math. Ind. 11, Paper No. 13, 46 p. (2021; Zbl 1490.93021) Full Text: DOI arXiv
Benner, Peter; Köhler, Martin; Saak, Jens Matrix equations, sparse solvers: M-M.E.S.S.-2.0.1 – philosophy, features, and application for (parametric) model order reduction. (English) Zbl 1480.93048 Benner, Peter (ed.) et al., Model reduction of complex dynamical systems. Selected papers based on the presentations at the workshop, University of Graz, Graz, Austria, August 28–30, 2019. Cham: Birkhäuser. ISNM, Int. Ser. Numer. Math. 171, 369-392 (2021). MSC: 93B11 93B25 93C05 93-04 PDFBibTeX XMLCite \textit{P. Benner} et al., ISNM, Int. Ser. Numer. Math. 171, 369--392 (2021; Zbl 1480.93048) Full Text: DOI arXiv
Chellappa, Sridhar; Feng, Lihong; La Rubia, Valentín De; Benner, Peter Adaptive interpolatory MOR by learning the error estimator in the parameter domain. (English) Zbl 1477.93124 Benner, Peter (ed.) et al., Model reduction of complex dynamical systems. Selected papers based on the presentations at the workshop, University of Graz, Graz, Austria, August 28–30, 2019. Cham: Birkhäuser. ISNM, Int. Ser. Numer. Math. 171, 97-117 (2021). MSC: 93B11 93C40 93C80 PDFBibTeX XMLCite \textit{S. Chellappa} et al., ISNM, Int. Ser. Numer. Math. 171, 97--117 (2021; Zbl 1477.93124) Full Text: DOI arXiv
Chellappa, Sridhar; Feng, Lihong; Benner, Peter A training set subsampling strategy for the reduced basis method. (English) Zbl 1502.65262 J. Sci. Comput. 89, No. 3, Paper No. 63, 34 p. (2021). MSC: 65N99 65F25 65D05 PDFBibTeX XMLCite \textit{S. Chellappa} et al., J. Sci. Comput. 89, No. 3, Paper No. 63, 34 p. (2021; Zbl 1502.65262) Full Text: DOI arXiv
Behr, Maximilian; Benner, Peter; Heiland, Jan Galerkin trial spaces and Davison-Maki methods for the numerical solution of differential Riccati equations. (English) Zbl 1510.65168 Appl. Math. Comput. 410, Article ID 126401, 28 p. (2021). MSC: 65L60 15A24 PDFBibTeX XMLCite \textit{M. Behr} et al., Appl. Math. Comput. 410, Article ID 126401, 28 p. (2021; Zbl 1510.65168) Full Text: DOI
Garmatter, Dominik; Maggi, Andrea; Wenzel, Marcus; Monem, Shaimaa; Hahn, Mirko; Stoll, Martin; Sager, Sebastian; Benner, Peter; Sundmacher, Kai Power-to-chemicals: a superstructure problem for sustainable syngas production. (English) Zbl 1471.92479 Göttlich, Simone (ed.) et al., Mathematical modeling, simulation and optimization for power engineering and management. Cham: Springer. Math. Ind. 34, 145-168 (2021). MSC: 92E20 93B11 93C20 PDFBibTeX XMLCite \textit{D. Garmatter} et al., Math. Ind. 34, 145--168 (2021; Zbl 1471.92479) Full Text: DOI
Feng, Lihong; Benner, Peter On error estimation for reduced-order modeling of linear non-parametric and parametric systems. (English) Zbl 1480.37086 ESAIM, Math. Model. Numer. Anal. 55, No. 2, 561-594 (2021). Reviewer: Hendrik Ranocha (Hamburg) MSC: 37M05 65P99 65L80 49Q12 PDFBibTeX XMLCite \textit{L. Feng} and \textit{P. Benner}, ESAIM, Math. Model. Numer. Anal. 55, No. 2, 561--594 (2021; Zbl 1480.37086) Full Text: DOI arXiv
Asif, Mian Mohammad Arsalan; Ahmad, Mian Ilyas; Benner, Peter; Feng, Lihong; Stykel, Tatjana Implicit higher-order moment matching technique for model reduction of quadratic-bilinear systems. (English) Zbl 1458.93040 J. Franklin Inst. 358, No. 3, 2015-2038 (2021). MSC: 93B11 93C10 PDFBibTeX XMLCite \textit{M. M. A. Asif} et al., J. Franklin Inst. 358, No. 3, 2015--2038 (2021; Zbl 1458.93040) Full Text: DOI arXiv
Benner, Peter; Goyal, Pawan Interpolation-based model order reduction for polynomial systems. (English) Zbl 1458.93041 SIAM J. Sci. Comput. 43, No. 1, A84-A108 (2021). MSC: 93B11 93C10 93C05 15A69 PDFBibTeX XMLCite \textit{P. Benner} and \textit{P. Goyal}, SIAM J. Sci. Comput. 43, No. 1, A84--A108 (2021; Zbl 1458.93041) Full Text: DOI arXiv
Kweyu, Cleophas; Feng, Lihong; Stein, Matthias; Benner, Peter Fast solution of the linearized Poisson-Boltzmann equation with nonaffine parametrized boundary conditions using the reduced basis method. (English) Zbl 07704919 Comput. Vis. Sci. 23, No. 1-4, Paper No. 15, 19 p. (2020). MSC: 65Nxx PDFBibTeX XMLCite \textit{C. Kweyu} et al., Comput. Vis. Sci. 23, No. 1--4, Paper No. 15, 19 p. (2020; Zbl 07704919) Full Text: DOI arXiv
Sima, Vasile; Benner, Peter Computational experience with a modified Newton solver for discrete-time algebraic Riccati equations. (English) Zbl 07627190 Gusikhin, Oleg (ed.) et al., Informatics in control, automation and robotics. 15th international conference, ICINCO 2018, Porto, Portugal, July 29–31, 2018, Revised selected papers. Cham: Springer. Lect. Notes Electr. Eng. 613, 142-167 (2020). MSC: 65-XX PDFBibTeX XMLCite \textit{V. Sima} and \textit{P. Benner}, Lect. Notes Electr. Eng. 613, 142--167 (2020; Zbl 07627190) Full Text: DOI
Benner, Peter; Du, Xin; Yang, Guanghong; Ye, Dan Balanced truncation of linear time-invariant systems over finite-frequency ranges. (English) Zbl 1467.93049 Adv. Comput. Math. 46, No. 6, Paper No. 82, 34 p. (2020). MSC: 93B11 93C05 93C80 PDFBibTeX XMLCite \textit{P. Benner} et al., Adv. Comput. Math. 46, No. 6, Paper No. 82, 34 p. (2020; Zbl 1467.93049) Full Text: DOI arXiv
Benner, Peter; Goyal, Pawan; Kramer, Boris; Peherstorfer, Benjamin; Willcox, Karen Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms. (English) Zbl 1506.93015 Comput. Methods Appl. Mech. Eng. 372, Article ID 113433, 17 p. (2020). MSC: 93B11 93C05 93C20 65M99 35K58 35K67 37M10 PDFBibTeX XMLCite \textit{P. Benner} et al., Comput. Methods Appl. Mech. Eng. 372, Article ID 113433, 17 p. (2020; Zbl 1506.93015) Full Text: DOI arXiv
Benner, Peter; Bujanović, Zvonimir; Kürschner, Patrick; Saak, Jens A numerical comparison of different solvers for large-scale, continuous-time algebraic Riccati equations and LQR problems. (English) Zbl 1437.65021 SIAM J. Sci. Comput. 42, No. 2, A957-A996 (2020). MSC: 65F45 65F55 15A24 PDFBibTeX XMLCite \textit{P. Benner} et al., SIAM J. Sci. Comput. 42, No. 2, A957--A996 (2020; Zbl 1437.65021) Full Text: DOI arXiv
Benner, Peter; Heinkenschloss, Matthias; Saak, Jens; Weichelt, Heiko K. Efficient solution of large-scale algebraic Riccati equations associated with index-2 DAEs via the inexact low-rank Newton-ADI method. (English) Zbl 1462.76142 Appl. Numer. Math. 152, 338-354 (2020). MSC: 76M99 76D05 PDFBibTeX XMLCite \textit{P. Benner} et al., Appl. Numer. Math. 152, 338--354 (2020; Zbl 1462.76142) Full Text: DOI arXiv
Ilyas Ahmad, Mian; Benner, Peter; Feng, Lihong A new two-sided projection technique for model reduction of quadratic-bilinear descriptor systems. (English) Zbl 1499.65362 Int. J. Comput. Math. 96, No. 10, 1899-1909 (2019). MSC: 65L80 65F99 PDFBibTeX XMLCite \textit{M. Ilyas Ahmad} et al., Int. J. Comput. Math. 96, No. 10, 1899--1909 (2019; Zbl 1499.65362) Full Text: DOI
Benner, Peter; Himpe, Christian Cross-Gramian-based dominant subspaces. (English) Zbl 1440.93043 Adv. Comput. Math. 45, No. 5-6, 2533-2553 (2019). MSC: 93B11 93B05 93B07 93C05 PDFBibTeX XMLCite \textit{P. Benner} and \textit{C. Himpe}, Adv. Comput. Math. 45, No. 5--6, 2533--2553 (2019; Zbl 1440.93043) Full Text: DOI arXiv
Benner, Peter; Braukmüller, Maike; Grundel, Sara A direct index 1 DAE model of gas networks. (English) Zbl 1416.78021 Keiper, Winfried (ed.) et al., Reduced-order modeling (ROM) for simulation and optimization. Powerful algorithms as key enablers for scientific computing. Cham: Springer. 99-119 (2018). MSC: 78M10 65N30 65L80 35Q31 76N15 35R02 05C20 34C20 PDFBibTeX XMLCite \textit{P. Benner} et al., in: Reduced-order modeling (ROM) for simulation and optimization. Powerful algorithms as key enablers for scientific computing. Cham: Springer. 99--119 (2018; Zbl 1416.78021) Full Text: DOI
Benner, Peter; Goyal, Pawan An iterative model reduction scheme for quadratic-bilinear descriptor systems with an application to Navier-Stokes equations. (English) Zbl 1416.76095 Keiper, Winfried (ed.) et al., Reduced-order modeling (ROM) for simulation and optimization. Powerful algorithms as key enablers for scientific computing. Cham: Springer. 1-19 (2018). MSC: 76M10 65N30 65M06 65L60 65L80 34C20 35Q30 76D05 65F15 65D05 PDFBibTeX XMLCite \textit{P. Benner} and \textit{P. Goyal}, in: Reduced-order modeling (ROM) for simulation and optimization. Powerful algorithms as key enablers for scientific computing. Cham: Springer. 1--19 (2018; Zbl 1416.76095) Full Text: DOI arXiv
Benner, Peter; Goyal, Pawan; Gugercin, Serkan \(\mathcal H_2\)-quasi-optimal model order reduction for quadratic-bilinear control systems. (English) Zbl 1418.93048 SIAM J. Matrix Anal. Appl. 39, No. 2, 983-1032 (2018). MSC: 93B11 93A15 93C10 49L99 35Q93 PDFBibTeX XMLCite \textit{P. Benner} et al., SIAM J. Matrix Anal. Appl. 39, No. 2, 983--1032 (2018; Zbl 1418.93048) Full Text: DOI arXiv
Baumann, Manuel; Benner, Peter; Heiland, Jan Space-time Galerkin POD with application in optimal control of semilinear partial differential equations. (English) Zbl 1392.35323 SIAM J. Sci. Comput. 40, No. 3, A1611-A1641 (2018). MSC: 35Q93 65L60 49M25 65M22 93C20 PDFBibTeX XMLCite \textit{M. Baumann} et al., SIAM J. Sci. Comput. 40, No. 3, A1611--A1641 (2018; Zbl 1392.35323) Full Text: DOI arXiv
Benner, Peter; Khoromskaia, Venera; Khoromskij, Boris N. Range-separated tensor format for many-particle modeling. (English) Zbl 1446.65202 SIAM J. Sci. Comput. 40, No. 2, A1034-A1062 (2018). MSC: 65P99 65F55 65F50 65N35 65F10 PDFBibTeX XMLCite \textit{P. Benner} et al., SIAM J. Sci. Comput. 40, No. 2, A1034--A1062 (2018; Zbl 1446.65202) Full Text: DOI arXiv
Benner, Peter; Mena, Hermann Numerical solution of the infinite-dimensional LQR problem and the associated Riccati differential equations. (English) Zbl 1444.65032 J. Numer. Math. 26, No. 1, 1-20 (2018). MSC: 65L06 65N12 49N05 93C20 93D15 PDFBibTeX XMLCite \textit{P. Benner} and \textit{H. Mena}, J. Numer. Math. 26, No. 1, 1--20 (2018; Zbl 1444.65032) Full Text: DOI Link
Ahmad, Mian Ilyas; Benner, Peter; Goyal, Pawan; Heiland, Jan Moment-matching based model reduction for Navier-Stokes type quadratic-bilinear descriptor systems. (English) Zbl 07775416 ZAMM, Z. Angew. Math. Mech. 97, No. 10, 1252-1267 (2017). MSC: 93Cxx 93Bxx 76Dxx PDFBibTeX XMLCite \textit{M. I. Ahmad} et al., ZAMM, Z. Angew. Math. Mech. 97, No. 10, 1252--1267 (2017; Zbl 07775416) Full Text: DOI
Benner, Peter; Stykel, Tatjana Model order reduction for differential-algebraic equations: a survey. (English) Zbl 1402.93069 Ilchmann, Achim (ed.) et al., Surveys in differential-algebraic equations IV. Cham: Springer (ISBN 978-3-319-46617-0/pbk; 978-3-319-46618-7/ebook). Differential-Algebraic Equations Forum, 107-160 (2017). MSC: 93B11 93C15 93B25 93-02 65F30 PDFBibTeX XMLCite \textit{P. Benner} and \textit{T. Stykel}, in: Surveys in differential-algebraic equations IV. Cham: Springer. 107--160 (2017; Zbl 1402.93069) Full Text: DOI
Benner, Peter; Goyal, Pawan; Redmann, Martin Truncated Gramians for bilinear systems and their advantages in model order reduction. (English) Zbl 1384.93028 Benner, Peter (ed.) et al., Model reduction of parametrized systems. Selected contributions based on the presentations at the MoRePaS conference, SISSA, Trieste, Italy, October 13–16, 2015. Cham: Springer (ISBN 978-3-319-58785-1/hbk; 978-3-319-58786-8/ebook). MS&A. Modeling, Simulation and Applications 17, 285-300 (2017). MSC: 93B11 93B05 93B07 93C10 93C15 PDFBibTeX XMLCite \textit{P. Benner} et al., MS\&A, Model. Simul. Appl. 17, 285--300 (2017; Zbl 1384.93028) Full Text: DOI
Benner, Peter; Dolgov, Sergey; Khoromskaia, Venera; Khoromskij, Boris N. Fast iterative solution of the Bethe-Salpeter eigenvalue problem using low-rank and QTT tensor approximation. (English) Zbl 1376.65045 J. Comput. Phys. 334, 221-239 (2017). MSC: 65F15 65F30 15A69 35Q35 PDFBibTeX XMLCite \textit{P. Benner} et al., J. Comput. Phys. 334, 221--239 (2017; Zbl 1376.65045) Full Text: DOI arXiv
Ahmad, Mian Ilyas; Benner, Peter; Goyal, Pawan Krylov subspace-based model reduction for a class of bilinear descriptor systems. (English) Zbl 1402.65083 J. Comput. Appl. Math. 315, 303-318 (2017). MSC: 65L80 34A09 93B11 93C05 PDFBibTeX XMLCite \textit{M. I. Ahmad} et al., J. Comput. Appl. Math. 315, 303--318 (2017; Zbl 1402.65083) Full Text: DOI Link
Benner, Peter; Kürschner, Patrick; Tomljanović, Zoran; Truhar, Ninoslav Semi-active damping optimization of vibrational systems using the parametric dominant pole algorithm. (English) Zbl 07775049 ZAMM, Z. Angew. Math. Mech. 96, No. 5, 604-619 (2016). MSC: 74P10 70J10 74G65 70Q05 PDFBibTeX XMLCite \textit{P. Benner} et al., ZAMM, Z. Angew. Math. Mech. 96, No. 5, 604--619 (2016; Zbl 07775049) Full Text: DOI
Benner, Peter; Saak, Jens; Uddin, M. Monir Structure preserving model order reduction of large sparse second-order index-1 systems and application to a mechatronics model. (English) Zbl 1348.93025 Math. Comput. Model. Dyn. Syst. 22, No. 6, 509-523 (2016). MSC: 93A15 93B11 93C15 93C95 PDFBibTeX XMLCite \textit{P. Benner} et al., Math. Comput. Model. Dyn. Syst. 22, No. 6, 509--523 (2016; Zbl 1348.93025) Full Text: DOI
Benner, Peter; Kürschner, Patrick; Saak, Jens Low-rank Newton-ADI methods for large nonsymmetric algebraic Riccati equations. (English) Zbl 1336.93056 J. Franklin Inst. 353, No. 5, 1147-1167 (2016). MSC: 93B40 93C15 93A15 65F10 PDFBibTeX XMLCite \textit{P. Benner} et al., J. Franklin Inst. 353, No. 5, 1147--1167 (2016; Zbl 1336.93056) Full Text: DOI
Benner, Peter; Kürschner, Patrick; Saak, Jens Frequency-limited balanced truncation with low-rank approximations. (English) Zbl 1391.65123 SIAM J. Sci. Comput. 38, No. 1, A471-A499 (2016). MSC: 65F60 15A16 15A18 15A24 93B11 93A15 PDFBibTeX XMLCite \textit{P. Benner} et al., SIAM J. Sci. Comput. 38, No. 1, A471--A499 (2016; Zbl 1391.65123) Full Text: DOI
Benner, Peter; Saak, Jens; Monir Uddin, M. Balancing based model reduction for structured index-2 unstable descriptor systems with application to flow control. (English) Zbl 1330.93084 Numer. Algebra Control Optim. 6, No. 1, 1-20 (2016). MSC: 93B40 93B11 93B18 65F30 65F50 PDFBibTeX XMLCite \textit{P. Benner} et al., Numer. Algebra Control Optim. 6, No. 1, 1--20 (2016; Zbl 1330.93084) Full Text: DOI
Benner, Peter; Bujanović, Zvonimir On the solution of large-scale algebraic Riccati equations by using low-dimensional invariant subspaces. (English) Zbl 1330.15017 Linear Algebra Appl. 488, 430-459 (2016). MSC: 15A24 15A18 15B57 65F15 65F30 PDFBibTeX XMLCite \textit{P. Benner} and \textit{Z. Bujanović}, Linear Algebra Appl. 488, 430--459 (2016; Zbl 1330.15017) Full Text: DOI
Benner, Peter; Gugercin, Serkan; Willcox, Karen A survey of projection-based model reduction methods for parametric dynamical systems. (English) Zbl 1339.37089 SIAM Rev. 57, No. 4, 483-531 (2015). MSC: 37M99 35B30 41A05 65K99 93A15 93C05 PDFBibTeX XMLCite \textit{P. Benner} et al., SIAM Rev. 57, No. 4, 483--531 (2015; Zbl 1339.37089) Full Text: DOI Link
Zhang, Yongjin; Feng, Lihong; Li, Suzhou; Benner, Peter An efficient output error estimation for model order reduction of parametrized evolution equations. (English) Zbl 1382.65281 SIAM J. Sci. Comput. 37, No. 6, B910-B936 (2015). MSC: 65M15 65D15 35L90 35K90 PDFBibTeX XMLCite \textit{Y. Zhang} et al., SIAM J. Sci. Comput. 37, No. 6, B910--B936 (2015; Zbl 1382.65281) Full Text: DOI Link
Benner, Peter; Redmann, Martin Model reduction for stochastic systems. (English) Zbl 1331.65017 Stoch. Partial Differ. Equ., Anal. Comput. 3, No. 3, 291-338 (2015). MSC: 65C30 60J75 60H15 60H10 34K28 93E25 PDFBibTeX XMLCite \textit{P. Benner} and \textit{M. Redmann}, Stoch. Partial Differ. Equ., Anal. Comput. 3, No. 3, 291--338 (2015; Zbl 1331.65017) Full Text: DOI
Mangold, Michael; Feng, Lihong; Khlopov, Dmytro; Palis, Stefan; Benner, Peter; Binev, Daniel; Seidel-Morgenstern, Andreas Nonlinear model reduction of a continuous fluidized bed crystallizer. (English) Zbl 1320.65132 J. Comput. Appl. Math. 289, 253-266 (2015). MSC: 65M20 65N08 76M12 76S05 82D25 PDFBibTeX XMLCite \textit{M. Mangold} et al., J. Comput. Appl. Math. 289, 253--266 (2015; Zbl 1320.65132) Full Text: DOI
Bänsch, Eberhard; Benner, Peter; Saak, Jens; Weichelt, Heiko K. Riccati-based boundary feedback stabilization of incompressible Navier-Stokes flows. (English) Zbl 1312.93083 SIAM J. Sci. Comput. 37, No. 2, A832-A858 (2015). MSC: 93D15 49M15 76D55 PDFBibTeX XMLCite \textit{E. Bänsch} et al., SIAM J. Sci. Comput. 37, No. 2, A832--A858 (2015; Zbl 1312.93083) Full Text: DOI Link
Benner, Peter; Breiten, Tobias Two-sided projection methods for nonlinear model order reduction. (English) Zbl 1312.93016 SIAM J. Sci. Comput. 37, No. 2, B239-B260 (2015). MSC: 93A15 93C10 93C15 15A69 PDFBibTeX XMLCite \textit{P. Benner} and \textit{T. Breiten}, SIAM J. Sci. Comput. 37, No. 2, B239--B260 (2015; Zbl 1312.93016) Full Text: DOI
Benner, Peter; Kürschner, Patrick Computing real low-rank solutions of Sylvester equations by the factored ADI method. (English) Zbl 1364.65093 Comput. Math. Appl. 67, No. 9, 1656-1672 (2014). MSC: 65F30 15A24 65F10 PDFBibTeX XMLCite \textit{P. Benner} and \textit{P. Kürschner}, Comput. Math. Appl. 67, No. 9, 1656--1672 (2014; Zbl 1364.65093) Full Text: DOI
Baur, Ulrike; Benner, Peter; Feng, Lihong Model order reduction for linear and nonlinear systems: a system-theoretic perspective. (English) Zbl 1348.93075 Arch. Comput. Methods Eng. 21, No. 4, 331-358 (2014). MSC: 93B17 PDFBibTeX XMLCite \textit{U. Baur} et al., Arch. Comput. Methods Eng. 21, No. 4, 331--358 (2014; Zbl 1348.93075) Full Text: DOI
Bänsch, Eberhard; Benner, Peter; Saak, Jens; Weichelt, Heiko K. Optimal control-based feedback stabilization of multi-field flow problems. (English) Zbl 1327.49061 Leugering, Günter (ed.) et al., Trends in PDE constrained optimization. Cham: Birkhäuser/Springer (ISBN 978-3-319-05082-9/hbk; 978-3-319-05083-6/ebook). ISNM. International Series of Numerical Mathematics 165, 173-188 (2014). MSC: 49N35 93B52 76D05 35Q30 PDFBibTeX XMLCite \textit{E. Bänsch} et al., ISNM, Int. Ser. Numer. Math. 165, 173--188 (2014; Zbl 1327.49061) Full Text: DOI
Grundel, Sara; Jansen, Lennart; Hornung, Nils; Clees, Tanja; Tischendorf, Caren; Benner, Peter Model order reduction of differential algebraic equations arising from the simulation of gas transport networks. (English) Zbl 1319.65077 Schöps, Sebastian (ed.) et al., Progress in differential-algebraic equations. Deskriptor 2013. Proceedings of the 8th workshop on coupled descriptor systems, Geseke, Germany, March 4–7, 2013. Berlin: Springer (ISBN 978-3-662-44925-7/hbk; 978-3-662-44926-4/ebook). Differential-Algebraic Equations Forum, 183-205 (2014). MSC: 65L80 34A09 90B10 90B06 PDFBibTeX XMLCite \textit{S. Grundel} et al., in: Progress in differential-algebraic equations. Deskriptor 2013. Proceedings of the 8th workshop on coupled descriptor systems, Geseke, Germany, March 4--7, 2013. Berlin: Springer. 183--205 (2014; Zbl 1319.65077) Full Text: DOI
Benner, Peter; Hossain, Mohammad-Sahadet; Stykel, Tatjana Low-rank iterative methods for periodic projected Lyapunov equations and their application in model reduction of periodic descriptor systems. (English) Zbl 1305.65158 Numer. Algorithms 67, No. 3, 669-690 (2014). MSC: 65K10 93C55 PDFBibTeX XMLCite \textit{P. Benner} et al., Numer. Algorithms 67, No. 3, 669--690 (2014; Zbl 1305.65158) Full Text: DOI Link
Benner, Peter; Voigt, Matthias A structured pseudospectral method for \(\mathcal {H}_{\infty}\)-norm computation of large-scale descriptor systems. (English) Zbl 1290.93083 Math. Control Signals Syst. 26, No. 2, 303-338 (2014). MSC: 93B60 93B36 93A15 93C15 93C05 PDFBibTeX XMLCite \textit{P. Benner} and \textit{M. Voigt}, Math. Control Signals Syst. 26, No. 2, 303--338 (2014; Zbl 1290.93083) Full Text: DOI
Benner, Peter; Ezzatti, Pablo; Quintana-Ortí, Enrique S.; Remón, Alfredo A factored variant of the Newton iteration for the solution of algebraic Riccati equations via the matrix sign function. (English) Zbl 1300.65021 Numer. Algorithms 66, No. 2, 363-377 (2014). Reviewer: Liu Xinguo (Qingdao) MSC: 65F30 65F10 15A24 PDFBibTeX XMLCite \textit{P. Benner} et al., Numer. Algorithms 66, No. 2, 363--377 (2014; Zbl 1300.65021) Full Text: DOI
Benner, Peter; Breiten, Tobias On optimality of approximate low rank solutions of large-scale matrix equations. (English) Zbl 1292.65040 Syst. Control Lett. 67, 55-64 (2014). MSC: 65F30 15A24 PDFBibTeX XMLCite \textit{P. Benner} and \textit{T. Breiten}, Syst. Control Lett. 67, 55--64 (2014; Zbl 1292.65040) Full Text: DOI
Benner, Peter; Börm, Steffen; Mach, Thomas; Reimer, Knut Computing the eigenvalues of symmetric \(\mathcal{H}^2\)-matrices by slicing the spectrum. (English) Zbl 1376.65044 Comput. Vis. Sci. 16, No. 6, 271-282 (2013). MSC: 65F15 65F50 15A18 65Y20 PDFBibTeX XMLCite \textit{P. Benner} et al., Comput. Vis. Sci. 16, No. 6, 271--282 (2013; Zbl 1376.65044) Full Text: DOI arXiv
Benner, Peter; Mach, Thomas The preconditioned inverse iteration for hierarchical matrices. (English) Zbl 1289.65074 Numer. Linear Algebra Appl. 20, No. 1, 150-166 (2013). Reviewer: Sabine Le Borne (Hamburg) MSC: 65F15 65F08 15B48 65F50 65N30 65N38 PDFBibTeX XMLCite \textit{P. Benner} and \textit{T. Mach}, Numer. Linear Algebra Appl. 20, No. 1, 150--166 (2013; Zbl 1289.65074) Full Text: DOI
Benner, Peter; Tomljanović, Zoran; Truhar, Ninoslav Optimal damping of selected eigenfrequencies using dimension reduction. (English) Zbl 1289.70028 Numer. Linear Algebra Appl. 20, No. 1, 1-17 (2013). Reviewer: Krešimir Veseli (Hagen) MSC: 70J10 34C15 34C46 PDFBibTeX XMLCite \textit{P. Benner} et al., Numer. Linear Algebra Appl. 20, No. 1, 1--17 (2013; Zbl 1289.70028) Full Text: DOI
Benner, Peter; Mach, Thomas The LR Cholesky algorithm for symmetric hierarchical matrices. (English) Zbl 1281.65051 Linear Algebra Appl. 439, No. 4, 1150-1166 (2013). MSC: 65F05 65F50 PDFBibTeX XMLCite \textit{P. Benner} and \textit{T. Mach}, Linear Algebra Appl. 439, No. 4, 1150--1166 (2013; Zbl 1281.65051) Full Text: DOI
Benner, Peter; Voigt, Matthias Spectral characterization and enforcement of negative imaginariness for descriptor systems. (English) Zbl 1278.93072 Linear Algebra Appl. 439, No. 4, 1104-1129 (2013). MSC: 93B25 65L80 15A22 15A23 PDFBibTeX XMLCite \textit{P. Benner} and \textit{M. Voigt}, Linear Algebra Appl. 439, No. 4, 1104--1129 (2013; Zbl 1278.93072) Full Text: DOI
Benner, Peter; Saak, Jens Numerical solution of large and sparse continuous time algebraic matrix Riccati and Lyapunov equations: a state of the art survey. (English) Zbl 1279.65044 GAMM-Mitt. 36, No. 1, 32-52 (2013). MSC: 65F30 15A24 65F10 65-02 PDFBibTeX XMLCite \textit{P. Benner} and \textit{J. Saak}, GAMM-Mitt. 36, No. 1, 32--52 (2013; Zbl 1279.65044) Full Text: DOI
Benner, Peter; Breiten, Tobias Low rank methods for a class of generalized Lyapunov equations and related issues. (English) Zbl 1266.65068 Numer. Math. 124, No. 3, 441-470 (2013). MSC: 65F30 PDFBibTeX XMLCite \textit{P. Benner} and \textit{T. Breiten}, Numer. Math. 124, No. 3, 441--470 (2013; Zbl 1266.65068) Full Text: DOI
Benner, Peter; Kürschner, Patrick; Saak, Jens Efficient handling of complex shift parameters in the low-rank Cholesky factor ADI method. (English) Zbl 1267.65047 Numer. Algorithms 62, No. 2, 225-251 (2013). Reviewer: R. P. Tewarson (Stony Brook) MSC: 65F30 65F10 15A24 65F50 PDFBibTeX XMLCite \textit{P. Benner} et al., Numer. Algorithms 62, No. 2, 225--251 (2013; Zbl 1267.65047) Full Text: DOI
Bänsch, Eberhard; Benner, Peter Stabilization of incompressible flow problems by Riccati-based feedback. (English) Zbl 1356.93077 Leugering, Günter (ed.) et al., Constrained optimization and optimal control for partial differential equations. Basel: Birkhäuser (ISBN 978-3-0348-0132-4/hbk; 978-3-0348-0133-1/ebook). ISNM. International Series of Numerical Mathematics 160, 5-20 (2012). MSC: 93D15 76D55 93C20 15A12 PDFBibTeX XMLCite \textit{E. Bänsch} and \textit{P. Benner}, ISNM, Int. Ser. Numer. Math. 160, 5--20 (2012; Zbl 1356.93077) Full Text: DOI
Benner, Peter; Breiten, Tobias Krylov-subspace based model reduction of nonlinear circuit models using bilinear and quadratic-linear approximations. (English) Zbl 1246.78035 Günther, Michael (ed.) et al., Progress in industrial mathematics at ECMI 2010. Proceedings of the 16th European conference on mathematics for industry, Wuppertal, Germany, July 26–30, 2010. Berlin: Springer (ISBN 978-3-642-25099-6/hbk; 978-3-642-25100-9/ebook). Mathematics in Industry 17, 153-159 (2012). MSC: 78M34 78A55 93B18 65H10 PDFBibTeX XMLCite \textit{P. Benner} and \textit{T. Breiten}, Math. Ind. 17, 153--159 (2012; Zbl 1246.78035) Full Text: DOI Link
Benner, Peter; Embree, Mark; Lehoucq, Richard B.; Kelley, C. T. A mathematical biography of Danny C. Sorensen. (English) Zbl 1238.01104 Linear Algebra Appl. 436, No. 8, 2717-2724 (2012). MSC: 01A70 PDFBibTeX XMLCite \textit{P. Benner} et al., Linear Algebra Appl. 436, No. 8, 2717--2724 (2012; Zbl 1238.01104) Full Text: DOI
Benner, Peter Partial stabilization of descriptor systems using spectral projectors. (English) Zbl 1250.93061 Van Dooren, Paul (ed.) et al., Numerical linear algebra in signals, systems and control. Selected papers based on the presentations at the international workshop, Kharagpur, India, January 9–11, 2007. In honor of Prof. Biswa Nath Datta. New York, NY: Springer (ISBN 978-94-007-0601-9/hbk; 978-94-007-0602-6/ebook). Lecture Notes in Electrical Engineering 80, 55-76 (2011). MSC: 93B55 93D15 93C05 93B40 15A22 PDFBibTeX XMLCite \textit{P. Benner}, Lect. Notes Electr. Eng. 80, 55--76 (2011; Zbl 1250.93061) Full Text: DOI
Benner, Peter; Faßbender, Heike On the numerical solution of large-scale sparse discrete-time Riccati equations. (English) Zbl 1230.65070 Adv. Comput. Math. 35, No. 2-4, 119-147 (2011). MSC: 65K10 49J20 49M15 49N10 65F30 15A24 PDFBibTeX XMLCite \textit{P. Benner} and \textit{H. Faßbender}, Adv. Comput. Math. 35, No. 2--4, 119--147 (2011; Zbl 1230.65070) Full Text: DOI
Benner, Peter; Ezzatti, Pablo; Kressner, Daniel; Quintana-Ortí, Enrique S.; Remón, Alfredo A mixed-precision algorithm for the solution of Lyapunov equations on hybrid CPU-GPU platforms. (English) Zbl 1225.65037 Parallel Comput. 37, No. 8, 439-450 (2011). MSC: 65F10 65F30 65Y05 PDFBibTeX XMLCite \textit{P. Benner} et al., Parallel Comput. 37, No. 8, 439--450 (2011; Zbl 1225.65037) Full Text: DOI
Benner, Peter; Faßbender, Heike; Stoll, Martin A Hamiltonian Krylov-Schur-type method based on the symplectic Lanczos process. (English) Zbl 1219.65040 Linear Algebra Appl. 435, No. 3, 578-600 (2011). Reviewer: R. Militaru (Craiova) MSC: 65F15 65F50 PDFBibTeX XMLCite \textit{P. Benner} et al., Linear Algebra Appl. 435, No. 3, 578--600 (2011; Zbl 1219.65040) Full Text: DOI
Benner, Peter; Mach, Thomas On the QR decomposition of \({\mathcal {H}}\)-matrices. (English) Zbl 1211.65049 Computing 88, No. 3-4, 111-129 (2010). MSC: 65F25 65F50 15A23 PDFBibTeX XMLCite \textit{P. Benner} and \textit{T. Mach}, Computing 88, No. 3--4, 111--129 (2010; Zbl 1211.65049) Full Text: DOI
Benner, Peter; Li, Ren-Cang; Truhar, Ninoslav On the ADI method for Sylvester equations. (English) Zbl 1176.65050 J. Comput. Appl. Math. 233, No. 4, 1035-1045 (2009). MSC: 65F30 15A24 40C05 37L99 PDFBibTeX XMLCite \textit{P. Benner} et al., J. Comput. Appl. Math. 233, No. 4, 1035--1045 (2009; Zbl 1176.65050) Full Text: DOI
Benner, Peter; Li, Jing-Rebecca; Penzl, Thilo Numerical solution of large-scale Lyapunov equations, Riccati equations, and linear-quadratic optimal control problems. (English) Zbl 1212.65245 Numer. Linear Algebra Appl. 15, No. 9, 755-777 (2008). MSC: 65K10 65F30 15A24 93C05 65F50 65H10 49N10 49N35 93B52 PDFBibTeX XMLCite \textit{P. Benner} et al., Numer. Linear Algebra Appl. 15, No. 9, 755--777 (2008; Zbl 1212.65245) Full Text: DOI
Benner, Peter Numerical linear algebra for model reduction in control and simulation. (English) Zbl 1157.93337 GAMM-Mitt. 29, No. 2, 275-296 (2006). MSC: 93B11 65F30 41A20 65F15 93-02 15A18 PDFBibTeX XMLCite \textit{P. Benner}, GAMM-Mitt. 29, No. 2, 275--296 (2006; Zbl 1157.93337) Full Text: DOI
Benner, Peter; Sokolov, Viatcheslav I. Partial realization of descriptor systems. (English) Zbl 1113.93026 Syst. Control Lett. 55, No. 11, 929-938 (2006). MSC: 93B11 93B20 93C05 93C15 PDFBibTeX XMLCite \textit{P. Benner} and \textit{V. I. Sokolov}, Syst. Control Lett. 55, No. 11, 929--938 (2006; Zbl 1113.93026) Full Text: DOI
Baur, U.; Benner, P. Factorized solution of Lyapunov equations based on hierarchical matrix arithmetic. (English) Zbl 1111.65039 Computing 78, No. 3, 211-234 (2006). Reviewer: Adhemar Bultheel (Leuven) MSC: 65F30 65F10 15A24 93B40 PDFBibTeX XMLCite \textit{U. Baur} and \textit{P. Benner}, Computing 78, No. 3, 211--234 (2006; Zbl 1111.65039) Full Text: DOI
Benner, Peter; Quintana-Ortí, Enrique S.; Quintana-Ortí, Gregorio Solving stable Sylvester equations via rational iterative schemes. (English) Zbl 1098.65041 J. Sci. Comput. 28, No. 1, 51-83 (2006). MSC: 65F30 15A24 65Y05 PDFBibTeX XMLCite \textit{P. Benner} et al., J. Sci. Comput. 28, No. 1, 51--83 (2006; Zbl 1098.65041) Full Text: DOI
Benner, Peter; Byers, Ralph An arithmetic for matrix pencils: theory and new algorithms. (English) Zbl 1101.65046 Numer. Math. 103, No. 4, 539-573 (2006). Reviewer: Liu Xinguo (Qingdao) MSC: 65F30 15A22 PDFBibTeX XMLCite \textit{P. Benner} and \textit{R. Byers}, Numer. Math. 103, No. 4, 539--573 (2006; Zbl 1101.65046) Full Text: DOI Link
Benner, Peter; Kressner, Daniel Balancing sparse Hamiltonian eigenproblems. (English) Zbl 1092.65026 Linear Algebra Appl. 415, No. 1, 3-19 (2006). Reviewer: Evgenij D’yakonov (Moskva) MSC: 65F15 65F50 PDFBibTeX XMLCite \textit{P. Benner} and \textit{D. Kressner}, Linear Algebra Appl. 415, No. 1, 3--19 (2006; Zbl 1092.65026) Full Text: DOI
Benner, P.; Quintana-Ortí, E. S.; Quintana-Ortí, G. Parallel algorithms for model reduction of discrete-time systems. (English) Zbl 1044.93012 Int. J. Syst. Sci. 34, No. 5, 319-333 (2003). Reviewer: Edwin Engin Yaz (Milwaukee) MSC: 93B11 93B40 93C55 65Y05 PDFBibTeX XMLCite \textit{P. Benner} et al., Int. J. Syst. Sci. 34, No. 5, 319--333 (2003; Zbl 1044.93012) Full Text: DOI
Benner, Peter; Quintana-Ortí, Enrique S.; Quintana-Ortí, Gregorio Numerical solution of discrete stable linear matrix equations on multicomputers. (English) Zbl 1009.65039 Parallel Algorithms Appl. 17, No. 2, 127-146 (2002). MSC: 65K10 15A24 93C55 94A08 65F30 93E11 65Y05 65Y20 PDFBibTeX XMLCite \textit{P. Benner} et al., Parallel Algorithms Appl. 17, No. 2, 127--146 (2002; Zbl 1009.65039) Full Text: DOI
Benner, Peter; Faßbender, Heike; Watkins, David S. \(SR\) and \(SZ\) algorithms for the symplectic (butterfly) eigenproblem. (English) Zbl 0947.65044 Linear Algebra Appl. 287, No. 1-3, 41-76 (1999). Reviewer: A.Ruhe (Göteborg) MSC: 65F15 65F50 PDFBibTeX XMLCite \textit{P. Benner} et al., Linear Algebra Appl. 287, No. 1--3, 41--76 (1999; Zbl 0947.65044) Full Text: DOI
Benner, Peter; Faßbender, Heike The symplectic eigenvalue problem, the butterfly form, the SR algorithm, and the Lanczos method. (English) Zbl 0935.65030 Linear Algebra Appl. 275-276, 19-47 (1998). MSC: 65F15 65F50 PDFBibTeX XMLCite \textit{P. Benner} and \textit{H. Faßbender}, Linear Algebra Appl. 275--276, 19--47 (1998; Zbl 0935.65030) Full Text: DOI
Benner, Peter; Mehrmann, Volker; Xu, Hongguo A new method for computing the stable invariant subspace of a real Hamiltonian matrix. (English) Zbl 1005.65034 J. Comput. Appl. Math. 86, No. 1, 17-43 (1997). Reviewer: J.P.Milaszewicz (Dublin) MSC: 65F15 15B57 15A24 PDFBibTeX XMLCite \textit{P. Benner} et al., J. Comput. Appl. Math. 86, No. 1, 17--43 (1997; Zbl 1005.65034) Full Text: DOI
Benner, Peter; Faßbender, Heike An implicitly restarted symplectic Lanczos method for the Hamiltonian eigenvalue problem. (English) Zbl 0884.65028 Linear Algebra Appl. 263, 75-111 (1997). Reviewer: A.Ruhe (Göteborg) MSC: 65F15 PDFBibTeX XMLCite \textit{P. Benner} and \textit{H. Faßbender}, Linear Algebra Appl. 263, 75--111 (1997; Zbl 0884.65028) Full Text: DOI