# Publications

Prof. Dr. Tatjana Stykel

### Books:

 [2] Model Reduction of Complex Dynamical Systems. P. Benner, T. Breiten, H. Faßbender, M. Hinze, T. Stykel, R. Zimmermann, eds., International Series of Numerical Mathematics, Vol.171, Birkhäuser, Cham, 2021. [1] Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory, Festschrift in Honor of Volker Mehrmann. P. Benner, M. Bollhöfer, D. Kressner, C. Mehl, T. Stykel, eds., Springer-Verlag, Berlin, Heidelberg, 2015.

### Submitted articles:

 [2] T. Reis, T. Stykel, Analysis of a quasilinear coupled magneto-quasistatic model. Part II: Passivity, port-Hamiltonian formulation and solution estimates. Hamburger Beiträge zur Angewandten Mathematik 2021-2, 2021. [1] R. Chill, T. Reis, T. Stykel, Analysis of a quasilinear coupled magneto-quasistatic model. Part I: Solvability and regularity of solutions. Hamburger Beiträge zur Angewandten Mathematik 2021-1, 2021.

### Refereed articles:

 [35] R. Altmann, D. Peterseim, T. Stykel, Energy-adaptive Riemannian optimization on the Stiefel manifold. ESAIM: M2AN, 2022, to appear. [34] N.T. Son, P.-A. Absil, B. Gao, T. Stykel, Computing symplectic eigenpairs of symmetric positive-definite matrices via trace minimization and Riemannian optimization. SIAM J. Matrix Anal. Appl., 42(4), 2021, pp. 1732-1757. [33] R. Pulch, A. Narayan, T. Stykel, Sensitivity analysis of random linear differential-algebraic equations using system norms. J. Comput. Appl. Math., 397, 2021, pp. 113666. [32] B. Gao, N.T. Son, P.-A. Absil, T. Stykel, Riemannian optimization on the symplectic Stiefel manifold. SIAM J. Optim., 31(2), 2021, pp. 1546-1575. [31] M.M.A. Asif, M.I. Ahmad, P. Benner, L. Feng, T. Stykel, Implicit higher-order moment matching technique for model reduction of quadratic-bilinear systems. J. Franklin Inst., 358(5), 2021, pp.2015-2038. [30] C. Berger, A. Fetzer, T. Stykel, S. Braunreuther, G. Reinhart, Stability analysis of a control-theoretic work system model. Procedia CIRP 83, 2019, pp. 642-648. [29] J. Kerler-Back, T. Stykel, Model reduction for linear and nonlinear magneto-quasistatic equations. Int. J. Numer. Meth. Engng, 111(13), 2017, pp. 1274-1299. (Preprint 14/2015, Universität Augsburg, 2015) [28] M. Baumann, A. Vasilyev, T. Stykel, P. Eberhard, Comparison of two model order reduction methods for elastic multibody systems with moving loads. Proc. IMechE Part K: J. Multi-body Dynamics, 231(1), 2017, pp. 48-56. [27] N.T. Son, T. Stykel, Solving parameter-dependent Lyapunov equations using the reduced basis method with application to parametric model order reduction. SIAM J. Matrix Anal. Appl., 38(2), 2017, pp. 478-504. [26] N. Lang, J. Saak, T. Stykel, Balanced truncation model reduction for linear time-varying systems. Math. Comput. Model. Dyn. Syst., 22(4), 2016, pp. 267-281. (Preprint CSC/15-05, TU Chemnitz, 2015) [25] T. Stykel, A. Vasilyev, A two-step model reduction approach for mechanical systems with moving loads. J. Comput. Appl. Math., 297, 2016, pp. 85-97. (Preprint 03/2015, Universität Augsburg, 2015) [24] N.T. Son, T. Stykel, Model order reduction of parameterized circuit equations based on interpolation. Adv. Comput. Math., 41(5), 2015, pp. 1321-1342. (Preprint 01/2014, Universität Augsburg, 2014) [23] P. Benner, M.-S. Hossain, T. Stykel, Low-rank iterative methods for periodic projected Lyapunov equations and their application in model reduction of periodic descriptor systems. Numer. Algorithms, 67, 2014, pp. 669-690. (Preprint CSC/11-01, TU Chemnitz, 2011) [22] P. Benner, T. Stykel, Numerical solution of projected algebraic Riccati equations. SIAM J. Numer. Anal., 52(2), 2014, pp. 581-600. [21] A. Steinbrecher, T. Stykel, Model order reduction of nonlinear circuit equations. Internat. J. Circuit Theory Appl., 41, 2013, pp. 1226-1247. (Preprint 2011/02, TU Berlin, 2011) [20] S. Gugercin, T. Stykel, S. Wyatt, Model reduction of descriptor systems by interpolatory projection methods. SIAM J. Sci. Comput., 35(5), 2013, pp. B1010-B1033. (Preprint 03/2013, Universität Augsburg, 2013) [19] M. Hinze, M. Kunkel, A. Steinbrecher, T. Stykel, Model order reduction of coupled circuit-device systems. Int. J. Numer. Model., 25, 2012, pp. 362-377. (Preprint 2011/11, TU Berlin, 2011) [18] T. Stykel, V. Simoncini, Krylov subspace methods for projected Lyapunov equations. Appl. Numer. Math., 62, 2012, pp. 35-50. (MATHEON Preprint 735-2010) [17] J. Möckel, T. Reis, T. Stykel, Linear-quadratic Gaussian balancing for model reduction of differential-algebraic systems. Internat. J. Control, 84(10), 2011, pp. 1627-1643. (Preprint 2011/01, TU Berlin, 2011) [16] J.C. De Los Reyes, T. Stykel, A balanced truncation based strategy for the optimal control of evolution problems. Optim. Methods Software, 26(4-5), 2011, pp. 673-694. (Preprint 2009/28, TU Berlin, 2009) [15] T. Reis, T. Stykel, Lyapunov balancing for passivity-preserving model reduction of RC circuits. SIAM J. Appl. Dyn. Syst., 10(1), 2011, pp. 1-34. (Preprint 2009/27, TU Berlin, 2009) [14] T. Reis, T. Stykel, PABTEC: Passivity-preserving balanced truncation for electrical circuits. IEEE Trans. Computer-Aided Design Integr. Circuits Syst., 29(9), 2010, pp. 1354-1367. [13] T. Reis, T. Stykel, Positive real and bounded real balancing for model reduction of descriptor systems. Internat. J. Control, 83(1), 2010, pp. 74-88. (Preprint 2008/25, TU Berlin, 2008) [12] T. Reis, T. Stykel, Balanced truncation model reduction of second-order systems. Math. Comput. Model. Dyn. Syst., 14(5), 2008, pp. 391-406. (MATHEON Preprint 376-2007) [11] T. Stykel, Low-rank iterative methods for projected generalized Lyapunov equations. Electron. Trans. Numer. Anal., 30, 2008, pp. 187-202. [10] T. Reis, T. Stykel, Stability analysis and model order reduction of coupled systems. Math. Comput. Model. Dyn. Syst., 13(5), 2007, pp. 413-436 (MATHEON Preprint 241-2005). [9] T. Stykel, A modified matrix sign function method for projected Lyapunov equations. Systems Control Lett., 56, 2007, pp. 695-701 (MATHEON Preprint 336-2006). [8] V. Mehrmann, T. Stykel, Descriptor systems: A general mathematical framework for modelling, simulation and control. at-Automatisierungstechnik, 54(8), 2006, pp. 405-415. [7] T. Stykel, On some norms for descriptor systems. IEEE Trans. Automat. Control, 51(5), 2006, pp. 842-847. [6] T. Stykel, Balanced truncation model reduction for semidiscretized Stokes equation. Linear Algebra Appl., 415(2-3), 2006, pp. 262-289. [5] T. Stykel, Gramian-based model reduction for descriptor systems. Math. Control Signals Systems, 16, 2004, pp. 297-319. [4] T. Stykel, Stability and inertia theorems for generalized Lyapunov equations. Linear Algebra Appl., 355, 2002, pp. 297-314. [3] T.Stykel, Numerical solution and perturbation theory for generalized Lyapunov equations. Linear Algebra Appl., 349, 2002, pp. 155-185. [2] T. Stykel, On criteria for asymptotic stability of differential-algebraic equations. Z. Angew. Math. Mech., 82(3), 2002, pp. 147-158. [1] T. Stykel, To the theory of degenerate systems of ordinary differential equations. Siberian Math. Journal, 36(5), 1995, pp. 1035-1049.

### Book chapters:

 [14] J. Kerler-Back, T. Stykel, Balanced truncation model reduction for 3D linear magneto-quasistatic field problems. In Realization and Model Reduction of Dynamical Systems - A Festschrift in Honor of the 70th Birthday of Thanos Antoulas, C. Beattie, P. Benner, M. Embree, S. Gugercin, S. Lefteriu, eds., Springer Proceedings in Mathematics and Statistics, Springer, 2021, to appear. (Preprint arXiv:1911.08798 [math.NA], 2019) [13] B. Gao, N.T. Son, P.-A. Absil, T. Stykel, Geometry of the symplectic Stiefel manifold endowed with the Euclidean metric. In Geometric Science of Information: GSI 2021, F. Nielsen, F. Barbaresco, eds., Lecture Notes in Computer Science, Vol. 12829, Springer Nature, Cham, Switzerland, 2021, pp.789-796. [12] N.T. Son, P.-Y. Gousenbourger, E. Massart, T. Stykel, Balanced truncation for parametric linear systems using interpolation of Gramians: a comparison of algebraic and geometric approaches. In Model Reduction of Complex Dynamical Systems, P. Benner, T. Breiten, H. Faßbender, M. Hinze, T. Stykel, R. Zimmermann, eds., International Series of Numerical Mathematics, Vol. 171, Birkhäuser, Cham, 2021, pp.31-51. [11] C. Hachtel, J. Kerler-Back, A. Bartel, M. Günther, T. Stykel, Multirate DAE/ODE-simulation and model order reduction for coupled field-circuit systems. In Scientific Computing in Electrical Engineering, U. Langer, W. Amrhein, W. Zulehner, eds., The European Consortium for Mathematics in Industry, Vol. 28, Springer International Publishing, 2018, pp. 91-100. [10] P. Benner, T. Stykel, Model order reduction of differential-algebraic equations: a survey. In Surveys in Differential-Algebraic Equations IV, A. Ilchmann, T. Reis, eds., Differential-Algebraic Equations Forum, Springer International Publishing, 2017, pp. 107-160. (Preprint MPIMD/15-19, MPI Magdeburg, 2015) [9] A. Steinbrecher, T. Stykel, Element-based model reduction in circuit simulation. In System Reduction for Nanoscale IC Design, P. Benner, ed., Mathematics in Industry, Vol. 20, Springer International Publishing, 2017, pp. 39-85. [8] T. Reis, T. Stykel, A Condensed Form for Nonlinear Differential-Algebraic Equations in Circuit Theory. In Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory, Festschrift in Honor of Volker Mehrmann. P. Benner, M. Bollhöfer, D. Kressner, C. Mehl, T. Stykel, eds., Springer-Verlag, Berlin, Heidelberg, 2015, pp. 503-531. [7] A. Steinbrecher, T. Stykel, Model order reduction of electrical circuits with nonlinear elements. In Progress in Industrial Mathematics at ECMI 2010, M. Günther, A. Bartel, M. Brunk, S. Schöps and M. Striebel, eds., Mathematics in Industry, Vol. 17, Springer-Verlag, Berlin, Heidelberg, 2012, pp. 169-177. [6] P. Benner, M.-S. Hossain, T. Stykel, Model reduction of periodic descriptor systems using balanced truncation. In Model Reduction for Circuit Simulation, P. Benner, M. Hinze and J. ter Maten, eds., Lecture Notes in Electrical Engineering, Vol. 74, Springer-Verlag, Berlin, Heidelberg, 2011, pp. 187-200. [5] T. Stykel, Balancing-related model reduction of circuit equations using topological structure. In Model Reduction for Circuit Simulation, P. Benner, M. Hinze and J. ter Maten, eds., Lecture Notes in Electrical Engineering, Vol. 74, Springer-Verlag, Berlin, Heidelberg, 2011, pp. 53-80. [4] T. Stykel, T. Reis, Passivity-preserving balanced truncation model reduction of circuit equations. In Scientific Computing in Electrical Engineering SCEE 2008, J. Roos and L.R.J. Costa, eds., Mathematics in Industry, Vol. 14, Springer-Verlag, Berlin, Heidelberg, 2010, pp. 483-490. [3] T. Reis, T. Stykel, A survey on model reduction of coupled systems. In Model Order Reduction: Theory, Research Aspects and Applications, W.H.A. Schilders, H.A. van der Vorst and J.Rommes, eds., Mathematics in Industry, Vol. 13, Springer-Verlag, Berlin, Heidelberg, 2008, pp. 133-155. [2] V. Mehrmann, T. Stykel, Differential equations and stability. In Handbook of Linear Algebra, L. Hogben, ed., Discrete Mathematics and Its Applications, CRC Press LLC, Boca Raton, FL, 2006, pp. 55/1-55/16. [1] V. Mehrmann, T. Stykel, Balanced truncation model reduction for large-scale systems in descriptor form. In Dimension Reduction of Large-Scale Systems, P. Benner, V. Mehrmann and D. Sorensen, eds., Lecture Notes in Computational Science and Engineering 45, Springer-Verlag, Berlin, Heidelberg, 2005, pp. 83-115.

### Technical reports, preprints:

 [5] P. Seiwald, A. Castagnotto, T. Stykel, B. Lohmann, ${\mathcal{H}}_{2}$ Pseudo-optimal reduction of structured DAEs by rational interpolation. Preprint arXiv:1804.08755 [math.NA], 2018. [4] D. Hömberg, A. Steinbrecher, T. Stykel, Optimal control of robot guided laser material treatment. Preprint 1405, WIAS Berlin, 2009. [3] F. Ebert, T. Stykel, Rational interpolation, minimal realization and model reduction. Preprint 371, DFG Research Center MATHEON, TU Berlin, 2007. [2] C. Schröder, T. Stykel, Passivation of LTI systems. Preprint 368, DFG Research Center MATHEON, TU Berlin, 2007. [1] T. Stykel, Input-output invariants for descriptor systems. Preprint PIMS-03-1, Pacific Institute for the Mathematical Sciences, Canada, 2003.

### Selected papers presented at workshops, conferences, congresses:

 [17] E. Massart, P.-Y. Gousenbourger, N.T. Son, T. Stykel, P.-A. Absil, Interpolation on the manifold of fixed-rank positive-semidefinite matrices for parametric model order reduction: preliminary results. Proceedings of the 27th European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning (ESANN 2019, Bruges, Belgium, April 24-26, 2019), ESANN, 2019. [16] J. Kerler, T. Stykel, Model order reduction for magneto-quasistatic equations. IFAC-PapersOnLine, Proceedings of the 8th Vienna International Conference on Mathematical Modelling (MATHMOD 2015, Vienna, Austria, February 18-20, 2015), 48(1), 2015, pp. 240-241. [15] N. Lang, J. Saak, T. Stykel, Towards practical implementations of balanced truncation for LTV systems. IFAC-PapersOnLine, Proceedings of the 8th Vienna International Conference on Mathematical Modelling (MATHMOD 2015, Viena, Austria, February 18-20, 2015), 48(1), 2015, pp. 7-8. [14] D. Kressner, P. Sirkovic, N.T. Son, T. Stykel, A low-rank reduced basis method for parameter-dependent Lyapunov equations. Proceedings of the 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS 2014, Groningen, The Netherlands, July 7-11, 2014), 2014. [13] J. Kerler, T. Stykel, Model reduction and dynamic iteration for coupled nonlinear systems. Proceedings in Applied Mathematics and Mechanics (GAMM 2014, Erlangen, March 10-14, 2014),14(1), 2014, pp. 527-528. [12] T. Stykel, C. Willbold, Model reduction based optimal control for field-flow fractionation. (GAMM 2013, Novi Sad, March 18-22, 2013) [11] T. Stykel, C. Willbold, Model reduction for optimal control problems in field-flow fractionation. Proceedings in Applied Mathematics and Mechanics (GAMM 2012, Darmstadt, March 23-30, 2012), 12(1), 2012, pp. 715-716. [10] T. Stykel, T. Reis, The PABTEC algorithm for passivity-preserving model reduction of circuit equations. Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2010, Budapest, Hungary, July 5-9, 2010), paper 363, 2010. [CD-Rom] [9] T. Reis, T. Stykel, Passivity-preserving model reduction of differential-algebraic equations in circuit simulation. Proceedings in Applied Mathematics and Mechanics (ICIAM 2007, Zürich, Switzerland, July 16-20, 2007), 7(1), 2007, pp. 1021601-1021602. [8] T. Stykel, Solving projected generalized Lyapunov equations with SLICOT. Proceedings of the IEEE CCA/CACSD/ISIC Conference 2006 (Munich, Germany, October 4-6, 2006), IEEE, 2006, pp. 14-18. [7] T. Stykel, Balancing-related model reduction of descriptor systems. Proceedings of the 6-th International Conference on Scientific Computing in Electrical Engineering (SCEE 2006, Sinaia, Romania, September 17-22, 2006), Printech, Bucuresti, 2006, pp. 17-18. [6] T. Stykel, Control problems for differential-algebraic equations. Workshop on Differential-Algebraic Equations (Oberwolfach, April 16-22, 2006), Oberwolfach Reports 18/2006, pp. 70-73. [5] T. Stykel, Balanced truncation model reduction of second-order systems. Proceedings of the 5th Vienna Symposium on Mathematical Modelling (MATHMOD 2006, Vienna, Austria, February 8-10, 2006), I. Troch and F. Breitenecker, eds., vol. 2, ARGESIM-Verlag, Vienna, 2006. [CD-Rom] [4] T. Stykel, Low rank iterative methods for projected generalized Lyapunov equations. Proceedings of the 16-th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2004, Leuven, Belgium, July 5-9, 2004), B. De Moore, B. Motmans, J. Willems, P. Van Dooren, V. Blondel, eds., Katholieke Universiteit Leuven, 2004. [CD-Rom] [3] T. Stykel, Balanced truncation model reduction for semidiscretized Stokes equation. The Eleventh Leslie Fox Prize Meeting, University of Cambridge, Cambridge, UK, June 20, 2003. (Photos) [2] T. Stykel, Balanced truncation model reduction for descriptor systems. Proceedings in Applied Mathematics and Mechanics (GAMM 2003, Abano Terme - Padua, Italy, March 24-28, 2003), 3(1), 2003, pp. 5-8. [1] V.I. Kostin, T. Stykel, Matrix spectrum dichotomy in boundary value problems for differential-algebraic equations. The Third Siberian Congress on Industrial and Applied Mathematics (INPRIM-98, Novosibirsk, Russia, June 22-27, 1998). Bulletin of Computer Center, Numerical Analysis, 1998.

### Other publications:

 [3] T. Stykel, Analysis and numerical solution of generalized Lyapunov equations. Ph.D. thesis, Institut für Mathematik, Technische Universität Berlin, 2002. [2] T. Stykel, Boundary value problems for implicit differential equations. Master thesis, Novosibirsk State University, 1996. [Russian] [1] T. Stykel, On computing the generalized Drazin inverse. Diploma thesis, Novosibirsk State University, 1994. [Russian]