Krylov subspaces associated with higher-order linear dynamical systems

BIT Numerical Mathematics

Volumn 45, Issue 3, 2005, Pages 495-516

  Freund, Roland W ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Higher order system; Krylov subspace; Linear dynamical system; Model reduction; Second order system

Indexed keywords

EID: 28144439377     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10543-005-0011-6     Document Type: Article

References (25)

1. J. I. Aliaga, D. L. Boley, R. W. Freund, and V. Hernández, A Lanczos-type method for multiple starting vectors, Math. Comp., 69 (2000), pp. 1577-1601.
2. Z. Bai, Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems, Appl. Numer. Math., 43 (2002), pp. 9-44.
3. Z. Bai and Y. Su, SOAR: A second-order Arnoldi method for the solution of the quadratic eigenvalue problem, SIAM J. Matrix Anal. Appl., 26 (2005), pp. 640-659.
4. Y. Chahlaoui, K. A. Gallivan, A. Vandendorpe, and P. Van Dooren, Model reduction of second order systems, in Dimension Reduction of Large-Scale Systems, P. Benner, V. Mehrmann, and D. C. Sorensen, eds., Springer-Verlag, 2005, pp. 149-172.
5. R. R. Craig, Jr. and A. L. Hale, Block-Krylov component synthesis method for structural model reduction, J. Guidance Control Dynam., 11 (1988), pp. 562-570.
6. R. A. DeCarlo, Linear Systems, Prentice-Hall, Englewood Cliffs, New Jersey, 1989.
7. R. W. Freund, Circuit simulation techniques based on Lanczos-type algorithms, in Systems and Control in the Twenty-First Century, C. I. Byrnes, B. N. Datta, D. S. Gilliam, and C. F. Martin, eds., Birkhäuser, Boston, 1997, pp. 171-184.
8. R. W. Freund, Krylov-subspace methods for reduced-order modeling in circuit simulation, J. Comput. Appl. Math., 123 (2000), pp. 395-421.
9. R. W. Freund, Model reduction methods based on Krylov subspaces, Acta Numer., 12 (2003), pp. 267-319.
10. R. W. Freund, SPRIM: structure-preserving reduced-order interconnect macromodeling, in Tech. Dig. 2004 IEEE/ACM International Conference on Computer-Aided Design, Los Alamitos, California, 2004, IEEE Computer Society Press, pp. 80-87.
11. R. W. Freund, Padé-type model reduction of second-order and higher-order linear dynamical systems, in Dimension Reduction of Large-Scale Systems, P. Benner, V. Mehrmann, and D. C. Sorensen, eds., Springer-Verlag, 2005, pp. 191-223.
12. I. Gohberg, P. Lancaster, and L. Rodman, Matrix Polynomials, Academic Press, New York, New York, 1982.
13. A. Graham, Kronecker Products and Matrix Calculus: with Applications, John Wiley & Sons, New York, New York, 1981.
14. R.-C. Li, Structural preserving model reductions, Technical Report 04-02, Department of Mathematics, University of Kentucky, Lexington, Kentucky, 2004.
15. R. Lozano, B. Brogliato, O. Egeland, and B. Maschke, Dissipative Systems Analysis and Control, Springer-Verlag, London, 2000.
16. J. Przemieniecki, Theory of Matrix Structural Analysis, Dover Publications, New York, New York, 1985.
17. G. X. Ren and Z. C. Zheng, A reformulated Arnoldi algorithm for non-classically damped eigenvalue problems, Int. J. Numer. Methods Eng., 40 (1997), pp. 3537-3555.
18. B. Salimbahrami and B. Lohmann, Order reduction of large scale second order systems using Krylov subspace methods, Linear Algebra Appl. To appear.
19. T.-J. Su and R. R. Craig, Jr., Model reduction and control of flexible structures using Krylov vectors, J. Guid. Control Dyn., 14 (1991), pp. 260-267.
20. D. F. Tuttle, Jr., Circuits, McGraw-Hill, Inc., New York, New York, 1977.
21. C. F. Van Loan, The ubiquitous Kronecker product, J. Comput. Appl. Math., 123 (2000), pp. 85-100.
22. A. Vandendorpe, Model reduction of linear systems, an interpolation point of view, PhD thesis, CESAME, Université catholique de Louvain, Louvain, Belgium, 2004.
23. A. Vandendorpe and P. Van Dooren, Krylov techniques for model reduction of second order system, Technical Report 07-2004, CESAME, Université catholique de Louvain, 2004.
24. T. Wittig, R. Schuhmann, and T. Weiland, Model order reduction for large systems in computational electromagnetics. Manuscript, 2003.
25. Z. C. Zheng, G. X. Ren, and W. J. Wang, A reduction method for large scale unsymmetric eigenvalue problems in structural dynamics, J. Sound Vib., 199 (1997), pp. 253-268.