Florida State University
Department of Mathematics



UCL

Mathematical Engineering



LIACS

Leiden University
Pascal Chair
Faculty of Science
Leiden Institute of Advanced Computer Science

Algorithms for Large-scale Dynamical Systems

  • [PDF File] K. A. Gallivan, A. Vandendorpe, and P. Van Dooren. Model Reduction and Sylvester Equations, Proceedings 2006 International Symposium on the Mathematical Theory of Networks and Systems, 2006, CD-ROM. pp. 1652--1664.

  • [PDF file] K. Gallivan, X. Rao, and P. Van Dooren. Singular Riccati Equations Stabilizing Large-scale Systems. To appear Linear Algebra and Its Applications.

  • [***] Y. Chahlaoui, K. A. Gallivan, A. Vandendorpe, and P. Van Dooren. Model Reduction of Second Order Systems. Dimension Reduction of Large-scale Systems, Lecture Notes in Computational Science and Engineering, Vol. 45, Springer-Verlag, P. Benner, V. Mehrmann, D. Sorensen, Eds., 2005, pp. 149-172.

  • [***] A. Antoulas, D. Sorensen, K. A. Gallivan, P. Van Dooren, A. Grama, C. Hoffmann, and A. Sameh. Model Reduction and Real-time Control Dynamic Data Driven Systems. To appear in: Dynamic Data Driven Application Systems, Kluwer Academic Publishers, Amsterdam, F. Darema, Ed.

  • [PDF file] K. Gallivan, A. Vandendorpe, and P. Van Dooren. Model reduction of MIMO Systems via Tangential Interpolation. SIAM Journal of Matrix Analysis and Applications, Vol. 26, No. 2, pp. 328 - 349, 2004.

  • [PDF file] A. Vandendorpe, K. Gallivan, and P. Van Dooren. Sylvester Equations and Projection-based Model Reduction, Journal of Computational and Applied Mathematics, Vol. 162, pp. 213-229, 2004.

  • [PDF file] Y. Chahlaoui, K. A. Gallivan, and P. Van Dooren. The H-infinity norm Calculation for Large Sparse Systems. Proceedings of 2004 International Symposium on Mathematical Theory of Networks and Systems, B. De Moor et al., Eds.

  • [PDF file] A. Antoulas, D. Sorensen, K. A. Gallivan, P. Van Dooren, A. Grama, C. Hoffmann, and A. Sameh. Model Reduction of Large-Scale Dynamical Systems. Proceedings 4th International Conference on Computational Science, Krakow, Poland, June 6-9, 2004, Part III, Lecture Notes in Computer Science, Vol. 3038, Bubak, M., Albada, G.D.V., Sloot, P.M.A., Dongarra, J., Eds., pp. 740-747.

  • [PDF file] K. Gallivan, A. Vandendorpe, and P. Van Dooren. Model Reduction via Truncation: An Interpolation Point of View, Linear Algebra and Its Applications, Vol. 375, pp. 115 - 134, 2003.

  • [PDF file] K. Gallivan, A. Vandendorpe and P. Van Dooren. Model Reduction via Tangential Interpolation, Proceedings of International Symposium on Mathematical Theory of Networks and Systems, 2002, University of Notre Dame, CD-ROM.

  • [PDF file] A. Vandendorpe, K. Gallivan, and P. Van Dooren. On the Generality of Multipoint Pade Approximations, Proceedings of 15th IFAC World Congress, 2002, CD-ROM.

  • [PDF file] X. Rao, K. A. Gallivan, and P. Van Dooren. Convergence Analysis of a Riccati-based Stabilization Method, Proceedings European Control Conference, 2001, CD-ROM.

  • [PDF file] X. Rao, K. A. Gallivan, and P. Van Dooren. Riccati Equation-based Stabilization of Large Scale Dynamical Systems. Proceedings IEEE 2000 Conference on Decision and Control, Sydney Australia, December 2000. CD-ROM.

  • [PDF file] X. Rao, K. A. Gallivan, and P. Van Dooren. Efficient Stabilization of Large Scale Dynamical Systems. Proceedings of IEEE International Symposium on Computer-Aided Control Systems Design, Anchorage USA, September 2000. CD-ROM.

  • [PDF file] X. Rao, K. A. Gallivan, and P. Van Dooren. Stabilization of Large Scale Dynamical Systems, Proceedings of International Symposium on Mathematical Theory of Networks and Systems, June 2000, Perpignan, France. CD-ROM.

  • [PDF file] K. A. Gallivan, E. Grimme and P. Van Dooren, Model reduction of large-scale systems: rational Krylov versus balancing techniques. In: Error Control and Adaptivity in Scientific Computing, Kluwer, Amsterdam, 1999, pp. 177-190, H. Bulgak and C. Zenger, Eds.

  • [PDF file] K. A. Gallivan and Paul Van Dooren. Rational Approximations of Pre-filtered Transfer Functions, Numerical Algorithms, No. 20, pp. 331-342, 1999.

  • [PDF file] D. S. Weile and E. Michielssen and E. Grimme and K. Gallivan. A Method for Generating Rational Interpolant Reduced Order Models of Two Parameter Systems, Applied Mathematics Letters. Vol. 12, pp. 93-102, 1999.

  • [PDF file] E. Grimme, K. A. Gallivan, P. M. Van Dooren. On Some Recent Developments in Projection-based Model Reduction. In: ENUMATH 97, Second European Conference on Numerical Mathematics and Advanced Applications, Y. Kuznetsov and J. Périaux, World Scientific, Singapore, 1998, pp. 98-113, H. Bock, G. Kanschat, R. Rannacher, F. Brezzi, R. Glowinsky, Eds.

  • [PDF file] K. Gallivan, E. Grimme, V. De Clippel, P. Van Dooren. Approximate Preconditioners in Krylov-based Modeling Methods, Proceedings of 36th Conference on Decision and Control, pp. 3849-3854, 1997.

  • [PDF file] K. Gallivan, E. Grimme, D. Sorensen, and P. Van Dooren. On some modifications of the Lanczos algorithm and the relation with Padé approximations, In: Mathematical Research Series, Vol. 7, Akademie Verlag, Berlin, 1996, pp. 87-116.

  • [PDF file] K. A. Gallivan, E. Grimme, and P. Van Dooren. A Rational Lanczos Algorithm for Model Reduction. Numerical Algorithms, Vol. 12, pp. 33-63, 1996.

  • [PDF file] K. Gallivan, E. Grimme, and P. Van Dooren. Asymptotic waveform evaluation via a Lanczos method. Applied Mathematics Letters, Vol. 7, pp. 75-80, 1994.

  • [PDF file] K. Gallivan, E. Grimme, and P. Van Dooren. Padé approximation of large-scale dynamical systems with Lanczos methods. Proceedings IEEE 33rd Conference on Decision and Control, pp. 443-448, 1994.