Publications

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Submitted articles

1. Inexact linear solves in the low-rank ADI iteration for large Sylvester equations, P.K., Arxiv e-print 2312.02891, 2023.

Articles in peer refereed journals

2. Systems of polynomial equations, higher-order tensor decompositions and multidimensional harmonic retrieval: a unifying framework. Part II: The block-term decomposition, Jeroen Vanderstukken, P.K., Ignat Domanov, Lieven De Lathauwer, SIAM J. on Matrix analysis and applications, 42(2):913–953, 2021; [preprint]

3. On the convergence of Krylov methods with low-rank truncations, Davide Palitta, P.K.; Numerical Algorithms, 88:1383–1417, 2021;  [preprint]

4. Numerical computation and new output bounds for time-limited balanced truncation of discrete-time systems,  Igor Pontes Duff, P.K.; Linear Algebra and its Applications,  623:367-397, 2021 (in Special Issue in Honor of Paul van Dooren) [preprint]

5. Inexact methods for the low rank solution to large scale Lyapunov equations, P.K., Melina Freitag; BIT Numerical Mathematics, 60:1221–1259, 2020 [preprint] [codes]

6. Low-rank updates and divide-and-conquer methods for quadratic matrix equations, Daniel Kressner, P.K., Stefano Massei; Numerical Algorithms, 84:717-741 , 2020 [preprint] 

7. A numerical comparison of solvers for large-scale, continuous-time algebraic Riccati equations and LQR problems, Peter Benner, Zvonimir Bujanović, P.K., Jens Saak; SIAM J. Sci. Comput., 42(2):A957–A996 , 2020 [preprint] [code/data]

8. Combined Error Estimates for Local Fluctuations of SPDEs; Christian Kuehn, P.K.; Advances in Computational Mathematics: 46(11), 2020   [preprint]

9. Greedy low-rank algorithm for spatial connectome regression; P.K., Sergey Dolgov, Kameron Decker Harris, Peter Benner;  The Journal of Mathematical Neuroscience: 9(1), Art. 9, 2019 [preprint] [code/data]

10. Approximate residual minimizing shift parameters for the low-rank ADI iteration, P.K.; Electronic Transactions on Numerical Analysis : 51:240-261, 2019    [preprint] 

11. RADI: A low-rank ADI-type algorithm for large scale algebraic Riccati equations; Peter Benner, Zvonimir Bujanović,  P.K., Jens Saak; Numerische Mathematik: 138(2):301–330, 2018  [preprint]

12. GMRES convergence bounds for eigenvalue problems ; Melina Freitag, P.K., Jennifer Pestana; Comput. Meth. Appl. Mat.:  18(2):203-222, 2018 [preprint]

13. Balanced truncation model order reduction in limited time intervals for large systems; P.K.; Advances in Computational Mathematics  :  44(6):1821-1844, 2018 [preprint] [codes]

14. An Output Error Bound for Time-Limited Balanced Truncation; Martin Redmann, P.K.; Syst. Control Lett.: 121:1-6, 2018 [preprint]  [codes]

15. Frequency-Limited Balanced Truncation with Low-Rank Approximations; Peter Benner, P.K., Jens Saak; SIAM J. Sci. Comput.:  38(1):A471-A499, 2016 [preprint]

16. Semi-active damping optimization of vibrational systems using the parametric dominant pole algorithm; Peter Benner, P.K., Zoran Tomljanović, Ninoslav, Truhar; ZAMM : 96(5):604-619, 2016 [preprint]

17. Low-Rank Newton-ADI methods for Large Nonsymmetric Algebraic Riccati Equations; Peter Benner, P.K., Jens Saak; Journal of The Franklin Institute  :  353(5):1147–1167, 2016 [preprint]

18. Tuned preconditioners for inexact two-sided inverse and Rayleigh quotient iteration; Melina Freitag, P.K.; Numerical Linear Algebra with Applications  :  22(1):175--196, 2015 [preprint]

19. Computing Real Low-rank Solutions of Sylvester equations by the Factored ADI Method; Peter Benner, P.K.; Computers and Mathematics with Applications  :  67(9):1656-1672, 2014  [preprint]

20. Self-Generating and Efficient Shift Parameters in ADI Methods for Large Lyapunov and Sylvester Equations; Peter Benner, P.K., Jens Saak; Electronic Transactions on Numerical Analysis :  43:142-162, 2014 [preprint]

21. Efficient Handling of Complex Shift Parameters in the Low-Rank Cholesky Factor ADI method; Peter Benner, P.K., Jens Saak; Numerical Algorithms: 62(2):225-251, 2013 [preprint]

22. Model Reduction of an Elastic Crankshaft for Elastic Multibody Simulations; Christine Nowakowski, P.K., Peter Eberhard, Peter Benner; ZAMM - Journal of Applied Mathematics and Mechanics: 93(4):198 - 216, 2013 [preprint]

23. An Improved Numerical Method for Balanced Truncation for Symmetric Second Order Systems; Peter Benner, P.K., Jens Saak; Mathematical and Computer Modelling of Dynamical Systems: 19(6):593-615, 2013 [preprint]

Articles in conference proceedings

1. Inner-outer methods for large-scale two-sided eigenvalue problems; Melina Freitag, P.K.; Numerical Solution of PDE Eigenvalue Problems  :  Oberwolfach Report 56/2013, 2013

2. A Reformulated Low-Rank ADI Iteration with Explicit Residual Factors; Peter Benner, P.K., Jens Saak; Proceedings in Applied Mathematics and Mechanics:  13(1):585–586, 2013

3. Improved second-order balanced truncation for symmetric systems; Peter Benner, P.K., Jens Saak; IFAC Proceedings Volumes:  45(2):758 - 762, 2012, Proceedings of 7th Vienna International Conference on Mathematical Modelling [preprint]

4. A Goal-Oriented Dual LRCF-ADI for Balanced Truncation, Peter Benner, P.K., Jens Saak; IFAC Proceedings Volumes:  45(2):752 - 757, 2012. Proceedings of 7th Vienna International Conference on Mathematical Modelling [preprint]

5. Avoiding complex arithmetic in the low-rank ADI method efficiently, Peter Benner, P.K., Jens Saak; Proceedings in Applied Mathematics and Mechanics: 12(1):639–640, 2012

6. Optimale FE-Reduktion, Moderne Modellreduktion elastischer Bauteile für die Simulation flexibler Mehrkörpersysteme (in German), Peter Benner, Peter Eberhard, Gunter Knoll, P.K., Christine Nowakowski, Gerard Ochse; FVV Frühjahrstagung 2011, Frankfurt a.M.: Forschungsvereinigung Verbrennungskraftmaschinen e.V.  :  Heft R553, pp. 175-197, 2011. 

7. Model order reduction of large-scale dynamical systems with Jacobi-Davidson style eigensolvers, Peter Benner, Michiel Hochstenbach, P.K.; International Conference on Communications, Computing and Control Applications, 2011 (CCCA11)  : IEEE; 2011, IEEE Catalog Number: CFP1154M-ART 

8. Two-sided harmonic subspace extractions for the generalized eigenvalue problem; Peter Benner, Michiel Hochstenbach, P.K.; Proceedings in Applied Mathematics and Mechanics: 11(1):741–742, 2011

Theses

1. Efficient Low-Rank Solution of Large-Scale Matrix Equations; P.K.; Shaker Verlag; PhD thesis, 2016. 

2. Two-Sided Eigenvalue Methods for Modal Approximation; P.K.; Master thesis, Chemnitz University of Technology; 2010. 

3. Der Jacobi-Davidson Algorithmus auf Parallelrechnern (in German), P.K.; Bachelor thesis, Chemnitz University of Technology; 2008.

Technical reports, misc.

1. Real versions of low-rank ADI methods with complex shifts; Peter Benner, P.K., Jens Saak; MPI Magdeburg Preprints MPIMD/12-11; 2012.